1. Do story lines continue from game to game?
2. What is the chronological orderings of the games?
3. Were are the new games set and how do they relate to each other and the first Pokemon Red?
4. Do the games relate to the TV Series?
5. I find this difficult to explain but I will try. The whole plot/scenarios and locations of Pokemon Red made sense to me but the new games confuse me because I don't understand were these new locations are, who new characters are and were these new Pokemon came from.
Collecting 150 Pokemon, Getting all 8 badges and becoming the Pokemon League Champion was the ultimate aim. So how has it developed from this?
1. The storylines don't really follow each other very closely. The better way to explain it is that each set of games focuses on a different character in the same world. Although, Gold(and Silver) take place a few years after Red(and blue.) The Black/White games take place before the Black2/White2 games. Some characters(like gym leaders and Prof Oak) make appearances in other games.
2. Timeline wise I'm not entirely sure, but the release order is how BraveNewWorld listed.
3. Each set of games(excluding the remakes) are set in a new region and the storylines have little to do with each other. The similarites to Red/Blue is that you still go around to collect badges, Pokemon, and fight the elite four while also taking out a Team. The newer games have more emphasis on the Teams doing something evil that include exploiting a Legendary Pokemon.
4. Not really, no. The anime is more influenced by the games if anything.
5. I feel your pain. I stopped playing Pokemon up until last year, so I completely missed Gens III and IV. If you can get your hands on a DS Lite, I suggest picking up a copy of FireRed. it's a remake of Red, follows that storyline with adding a little bit more at the end, but also has the updated graphics for the Advance games.
Getting FireRed should also get you accustomed to the new features in the battling system such as Pokemon Abilities and Moods in an environment you're familiar with. Black and White would be my suggestion to play afterwards because you only encounter Gen V Pokemon, and Gens I-IV are absent for most of the game so you can get yourself use to this new set, and slowly work your way from there.