[Discussion] How to make a Randomizer Nuzlocke fair and challenging

Change Impossible Evolutions is pretty much required, and you can even do in your normal nuzlocke if you don't want to use PKHex to evolve your trade mons, same goes for Remove Time-Based Evolutions for FRLG (in which case you gotta turn on give national dex from the start).

Random starters is pretty cool, just don't pick something too strong to begin with.
Randomizing stactic Pokémon to those of similar strength usually results in the same thing as switching a legendary stactic with another legendary, since they always have high stats like that, though it can also reward you with a pseudo legendary, which is pretty funny.
Randomized trades will rarely come up, but it's extremely funny when they do, so I turn that on to the max.

Trainer Pokémon should always be randomized with gyms and e4 type themed, after all, what's the fun if they aren't?
Double battle mode is interesting, and you can totally go for it, it's pretty fun! It really just depends on what kind of player you are. I personally prefer having the option on, but it's understandable not to have it.
Better movesets is a must, otherwise Pokémon will have their level up movesets, leading to a really easy run due to the oponents just not having good moves, always opting to delete old ones. Careful though, this makes so that the Pokémon have some often pretty strong TM and egg moves, so you gotta be extra careful with this on.
Giving item to boss and important trainers may be really important depending on the game (like the gen 3 games who rarely give items to trainers), but I'd say for gen 5 it's fairly pointless, specially on challenge mode. Up to you though.
Rival carries starter and No early Wonder Guard are some admitedly minor things, but they're pretty fun to have.
And now, for the controversial one. In my opinion, you should always turn on Try to Use Pokémon with similar strength, and this goes for not only trainers, but also wild Pokémon. Without this, you'll get the unfair nuzlocke experience that's associated with Randomizer Nuzlockes. You'll get utterly unwinnable encounters with Pokémon like Groudon or Giratina, while only having Pokémon like Exeggcute by your side. Without this all you'll get is one of those randomizer nuzlockes that Youtubers do that are actually really entertaining but is pretty frustating to actually experience.
Forcing fully evolved Pokémon can come at either level 30 or 35, really depends on the game.

Having TMs and Move Tutors being random is REALLY FUNNY, but is kinda broken post gen 4, where you can use TMs infinitively. Gen 3 and before should be fine though.

Special shops should only be random in order to allow you to get guaranteed evolution items, in case you either cannot get them in the base game, or have turned on Field Items to random, which would make getting the previously easy to get evo items impossible.

Updating type effectivenes can either make the game much easier or much harder for you in some cases, so it's up to you and the generation you're playing to decide. Personally I would do it gen 1, where Psychic types were simply too strong, but at the same time, I could see myself not using, and instead banning psychic types to make the game harder, it really depends.
One last thing: Pleaaaase turn on Fastest Text bro no one can handle so much as fast speed anymore, we need to go maximum speed.