I would

no

So this gamr is never on when im out the house but soon i come home s3rver is fine

Any benefits to leaving a Pokémon at a gym (not as a gym leader)?

If I did leave a Pokémon at a gym, how would the CP of that Pokémon affect anything?

If your Pokemon is part of the gym defending it I believe you still get the rewards. An attacker has to go through all Pokemon to take it over so yours will help in that way

So has it been mentioned here that you can choose which eevee evolution it goes to?

Like every 20 pages

If you're in the gym you're considered a gym leader and still get the reward.
Me n gf go get numerous gyms then we both collect same reward no matter who is the leader.

Oh... well then... Hey guys you just have to rename them

Yeah collect your rewards on the shop page I believe.