Goodness. I assume you are looking for advice for the game, not for competitive battling, so I'll leave my two cents.
For Mr. Krabs, you are right that you probably don't need two water types on your team. He already has three HM moves already, so since you seem to like Gyarados better you might want to teach Mr. Krabs Rock Smash or another HM move and use him just for getting from place to place.
For Drowzee, he probably seems weak because he has terrible, terrible moves. Zen Headbutt would do wonders for your drowzee, but so could Hypnosis and Dream Eater. Drowzee's best stat is its Special Defense, so it would be best at walling a Hyper Beam for example. If you were to let Drowzee have another chance, I'd recommend getting rid of Pound, and Headbutt, at LEAST. I'd get rid of Focus Punch too, but Focus Punch could be really awesome paired with Hypnosis.
HOWEVER since you seem so keen on getting rid of Drowzee, I'll suggest some replacements. One good one might be Girafarig, since it can learn both Special and Physical moves and use them well. The bad part about Girafarig is that it doesn't have great stats, especially its defenses. A better replacement would be Jynx, which you can find in Ice Path (or evolve from Smoochum if you get the daycare couple to give you its egg, which it looks like you haven't done yet). Jynx gets Psychic and Blizzard, both very powerful moves. I've used one before and it was one of the best members of my team when I played Crystal. You just have to be careful not to use it against Dark or Fire types, but it should help you plow right through the Dragon Gym. If you can get ahold of an Abra, its evolutions (Kadabra and Alakazam) are very strong, but it is a pain to train.
For Shuckle... that is a very terrible moveset. But you're right, Shuckle doesn't really have great stats. It has AMAZING defense, but that's about it. With the right moves, Shuckle can switch its attack and defense, giving it AMAZING attack, but that is honestly not very practical for just playing through the game. So replacing it is a good choice.
If you are looking for another rock type to replace Shuckle... I want to say Armaldo, but that would be hard to get. You can get Rhyhorn at the Safari Zone. Teach it Stone Edge and Earthquake, and it will do great damage. Just keep it away from grass, water, and fighting types. Rhyhorn's rock moves can easily take out Ice Types, but it is hurt by ice moves too so be careful. If you don't want to use Rhyhorn, you could try Swinub. If you evolve it into Mamoswine (evolve it into Piloswine, then get the move tutor to teach it Ancientpower) it gets really strong moves like Ice Shard, Avalanche, and Earthquake. However, you may NOT want to use Mamoswine AND Jynx because they are both weak to rock moves.
Bellsprout... My gosh, those moves are pretty terrible. If you want to use your Bellsprout for battle, I suggest going to the Move Deleter in Blackthorne and getting rid of Flash and Cut right away. Poisonpowder is good, but you need something to do damage. Vine Whip, Razor Leaf, Sludge Bomb, Energy Ball, SOMETHING. It will do much better in battle if it has an attacking move that matches its type. Whether you keep Attract or not is up to you, but it is very situational and there are probably much more useful moves you could use in its place.
Gyarados, also has terrible moves, but you just caught it so it's understandable. None of those moves are ones you want to keep, though Bite is the best of what you have in my opinion. In two levels Gyarados will learn Ice Fang, DEFINITELY LEARN THIS. With it you can easily take down dragon types, flying types, and grass types. Next, teach it Waterfall as soon as you can, or if not that, then Aqua Tail (which it learns at level 35). The other moves are not as important, but Gyarados can learn a lot of good ones like Stone Edge, Earthquake, and Bounce. I'd teach it Bounce if you can, since Gyarados is Flying type. Gyarados's only real weakness is electric, so either keep it away from electric types or teach it earthquake to kill them with. (Lastly, it's rather unfortunate that your Gyarados has a Modest nature, because this lowers its attack stat and raises it's rather poor special attack stat. It won't be as powerful as an Adamant Gyarados, but I think you'll still find that it's still very powerful.)
Ah, Typhlosion. It's clear that you rely on this pokemon whenever you have trouble, since it's level 50 and the others are around level 15 or 20. Get rid of Rock Smash when you can, and give that to Krabby if it can learn it. Flamethrower is the best move you have here, and it makes Flame Wheel and Lava Plume redundant. I put Dig on my Typhlosion, which was really helpful when dealing with anything that didn't die so quickly to fire (though Typhlosion can learn earthquake as well). You may also want to teach it thunderpunch in case it gets stuck fighting a water type. Or, instead of Thunderpunch, you may want to teach it Sunny Day and Solarbeam. Sunny Day will boost the power of Typhlosion's fire moves, and let you use Solarbeam without charging. That way, any rock or water types that try to stand in your Typhlosion's way get shot down with Solarbeam. Try to stick with special attacks when possible: Typhlosion is generally better with special attacks, but your typhlosion's Bold nature makes this even more true (its attack stat is weaker and its defense stat is stronger than normal).
For your playstyle, I'd guess that Togepi probably isn't worth it. Togekiss, its final form, often relies on slowly whittling down your opponents health while making them flinch. It's a good strategy, but you seem to like to take down pokemon fast (EDIT: This is a pretty big assumption, so sorry if that is wrong), which is usually not what Togekiss is good at. One suggestion I have for your team is adding a pokemon that can learn Fly. Fly is one of the few HM moves that is also a good attack, and the ability to fly to any town you've been in an instant is SO useful. If you decide to put a flying type on your team, I can recommend Spearow and (you won't believe it) Zubat. Spearow is a good attacking pokemon, and evolves into Fearow at level 20. It is fast and hits hard, and also learns Roost (which lets it heal itself without you using an item). If you have the patience, though, Crobat may be the better option. If you evolve your zubat into Golbat, train it a lot and get it to love you (DON'T let it faint, DON'T give it herbal medicine, DO give it massages, DO carry it with you, DO use items on it) then it will evolve into Crobat. Crobat's attack is just as strong as Fearow's, but it is even faster and has better defenses. Crobat also learns a lot of good moves. Try to stick to physical moves, and have at least one physical flying move (eg. Fly) and one physical poison move (eg. Poison Jab) on it if you use it. Also give it X-scissor to take out psychic types (which both Crobat and Victreebel are weak against). Also keep in mind that both Crobat and Fearow are weak against rock and ice types! EDIT: However, both are good against fighting and grass types!
Well, that'll probably be a big wall of text. My suggestion to you, if you want to have a TEAM of pokemon that are strong enough to actually *help* your typhlosion, is to train them! Don't just let them faint and then switch in your Typhlosion when things are looking bad. Send them out, then switch them to something that can defeat the opponent. If you really want to commit to having a lot of strong pokemon, and not just your Typhlosion, I would suggest putting it in a box and not taking it out until the rest of your pokemon have reached the same level. That's up to you, of course.
Remember, any pokemon can be strong with the proper moves and the proper training. I hope this was helpful at all. Good luck!
EDIT2: Sorry if I assumed too much. I've never done one of these team-rating things before! Let me know if I was completely off-base.
EDIT: You wanted us to post our teams, so I guess I'll post mine so you can see. I played my game weirdly, so I ended up with a 7-pokemon team. It made training take a little longer. x.x;
Let's see if I can do this from memory:
Qilu/Girafarig
Normal/Psychic
Level 64~
Ability: Inner Focus?
Agility
Baton Pass
Psychic
Return
Qilu is sadly one of the weakest members of my team. She knows two strong moves that match her types, which lets her do fairly good damage. However, I usually use super-effective attacks whenever possible, so she doesn't see a lot of usage. However, she can baton-pass a speed boost to another pokemon, which can be really useful.
Peccadillo/Armaldo
Rock/Bug
Level 64~
Ability: Battle Armor
Swords Dance
Stone Edge
X-Scissor
Headbutt? (don't quite remember)
I seriously love Pecadillo. He's got good type coverage, and Swords Dance makes his attack strong enough to take down almost anything. However, he's really slow, and is unfortunately weak to water and rock. With a little help from Qilu, though, he can be quite the monster.
Lufte/Tropius
Grass/Flying
Level 64~
Ability: Solar Power
Air Slash
Fly
Synthesis?
Leaf Storm
Lufte is another weaker member of the team, mostly because of her typing. I'm never sure if I can safely put her against water types, since she's so weak to ice moves. I think she's also weak to rock. But still, she has her moments, and Tropius is one of my favorite pokemon.
Carnot/Rotom
Ghost/Electric
Level 64~
Ability: Levitate
Air Slash
Discharge
Confuse Ray
Thunder Wave
Carnot is usually in his fan form, which lets him have Air Slash. I don't remember how, but Carnot did most of the work when I fought Red. I don't know what I would've done without him. He wasn't really that great when I got him (hatched him from an egg) but over time he's become one of the best in my team. If he can't easily take something out with discharge or air slash, I'll usually have him use thunder wave, confuse ray, and air slash, stacking up the odds that the opponent won't be able to attack back at all, and watching them slowly die.
Truffle/Mamoswine
Ice/Ground
Level 64~
Ability: Oblivious? (don't remember)
Ice Shard
Earthquake
Avalanche
Endure
Truffle has the same deal going as Carnot, he wasn't great at first but over time has become one of the best members of my team. Also, I'd like to mention that I hated Mamoswine before I got Truffle, but now I don't think it's so bad. (Truffle is the only one of this team who I didn't hatch from an egg)
Ruka/Lucario
Steel/Fighting
Level 64~
Ability: Inner Focus?
(I DON'T REMEMBER but here's my best guess)
Endure
Reversal
Aura Sphere
Extremespeed
Ruka is mainly here because I needed a fighting type and a steel type for the run I was doing. She is a stronger fighter than Qilu, so those two are the ones I usually swap for eachother. Lucario is a pretty good pokemon, but not one of my favorite since it's so mainstream.
Murru/Kingdra
Water/Dragon
Level 65~
Ability: Sniper
Surf
Brine
Dragon Pulse
Signal Beam
Murru was my "starter" (I chose totodile, then booted it out for my newly-hatched Horsea the first chance I got). Signal Beam and Octazooka were her egg moves, since I got her from a friend. I mostly have Brine there 'cause it's a little stronger than surf in the right situations, but I should probably replace it for Ice Beam or something. Murru is a great pokemon and has never let me down. :3
Uh, yeah, so that's my team if that helps you at all. I don't remember the levels exactly, but I knew they were all around level 65, and that I like to keep Murru one level higher than the rest. An important thing to keep in mind when making any team is that your pokemon should try to cover eachothers' weaknesses. I think mine does that fairly well.