Well... There is actually unlimited eggs because you can breed any time you want at the pokemon daycare but there is one egg you can get without breeding. At route 18 you will get a larvesta egg from a man.
Only a traded Manaphy, which will produce Phione eggs.
No.
You should only be handed one, but with breeding the numbers are infinite.
the only level one pokemon you can get is pokemon from eggs.
Yes if they are in eggs.
no
You get a certain Pokemon that cuts the steps you walk but it depends on the old versin of black or the new versin
Have a Pokemon who's ability is flamebody at the head of your party
Yes, you can by putting mew and mewtwo in the darecare together their eggs will have mewthree in it
yes if you breed one with a ditto they can make eggs
Actually I don't think anyone knows. Its kinda weird, plus I'm just guessing
1