If you talk to someone in the Game Freak building he will give you a certificate.
Complete the Unova pokedex (after that coplete the national pokedex)
complete your national pokedex, of course
you defeat team plasma and get the national dex,then battle alder
Nothing happens after you get the National Pokedex, but there are other things to do, such as looking for the Seven Sages, visiting parts of the Unova Region now accessible,...etc.
At your home
You could buy pokemon black and white
If you complete Pokemon Black, you must find your way to the PokeTransfer lab. This will enable you to transfer Pokemon DS Game Pokemon to Pokemon Black, though you will need two DSs to complete the process. So basically yes.
There are 649 pokemon.
you can't
it is Uxie before the national dex and Moltres after you get the national dex
649 [including Pokemon black and white]
Unova Pokedex: Landorus National Dex: Mew