There are 1 billion EOS tokens, is everything mined since its a POS system? If not, how much is already mined? And where are block producers getting their coins from?
The monetary inflation system of a blockchain is independent of whether the consensus algorithm is based on proof of work or proof of stake.
EOS mainnet has more than 1 billion tokens, as new tokens are minted in every block. There is no supply-cap, and a 1% inflation per year is planned to reward BPs. Further, there is another 4% inflation per year that is locked in some contracts until the community decides what should happen with it (current proposals include funding EOS projects, burning the tokens, allocating them to those lending EOS, and probably others)
To answer your question:
Are all of the EOS tokens already mined since its a POS system?
No, the supply is uncapped and EOS tokens will continue to be created at a fixed rate. Part of the block reward goes to financing the block producers, and part of it is yet to be decided where it shall go.