Is there a limit of how many draft picks I can have in a year? I am thinking of investing in a lot of draft picks.

I'd advise against this strategy unless you're very experienced at this game. First off, draft picks are overvalued in this league. You're likely not going to get back in picks all of the value you trade away. If you're looking to rebuild, go ahead and trade your 9+ year players for carefully selected picks, but don't bank your whole long term plan on it.

Also, rookie contracts are more expensive than the player is worth in this game, so you could get yourself in to cap trouble. Keep trying to build through free agency.