Is it possible to get coins in both chains? Does that mean that you get "free" BC2 or whatever the name they choose? If so, how can I make sure I am in?
If you own bitcoin, you already own coin in the original blockchain. Whatever is airdropped from the segwit2x hardfork will deliver you coins in the second chain. Both can exist in parallel (e.g., bitcoin cash exists along side bitcoin).
What you need to do make sure you acquire the new coin is:
1. Have your bitcoin in a wallet where you control your private keys, or
2. Have your bitcoin in an exchange wallet that will support the new coin
Some time after the fork you'll be able to claim your version of the new coin and do with it what you will - sell or hodl.