Can I Get Mew In Leaf Green?

Yes, you can, but you have to beat the elite four 12 times and then go back to the place where you catch mewtwo. Run around there and you will find mew. :-)

No, but you can trade for a mew from Emerald, where you need a secret map from nintendo wonder mail to travel to a faraway island.

Yes, here is the code for mew but if you don't know how to use it first you have to open the cheat list and click on code breaker and put the code
00000554 000A
1003dae6 0007
83007CEE
0097
then click on OK , and go to a grass walk until there is wild pokemons, but when you're done catching it click again in the cheat list and click on the check ... Good luck