Answer 1
If someone registers your FC, it will count that they have two seperate friends, instead of just 1
Answer 2
Nothing will happen.
Answer 3
You can trade on the GTS as soon as you catch a second Pokémon, as it won't allow you to trade your starter without another Pokémon in your party.
PSS can be used for communication and battles as soon as you get your starter.
Sources:
Answer 1-Knowledge
Answer 2-Knowledge
Answer 3-This