Visit Lavender town, you will find in the most southern house
Chat with our AI personalities
I don't belive you can.
Go to the house next to the Poke Mart in Eterna City. Talk to the old man and he will change your pokemon's nickname. Sadly, you cannot change the name of trade pokemon.
Yes you can trade leafgreen version Pokemon to another leafgreen version.
Some people say to nickname your starter Pokemon "Mew" and it will play as mew for the rest of the game but I never tested it...
You can go to the name rater in Lavender.