I was wondering what happens if multiple forks happen and you don't bother with moving your coins to access the coins on the other chains? Am I safe by not doing nothing?
Now with BGold, I will have coins too on the BGold chain, on the same addresses as the Bitcoin chain and BCash chain. So that's 3 different tokens on 3 different blockchains sitting on the same addresses. Is there any problem with that?
Depends. The main problem with having coins with similar blockchain and transaction formats means that a transaction can be valid on all of the chains. This means that if you send a coin on the BTC blockchain from a BTC address to a BTC address, you can also be sending coins on a BCH address, from a BCH address to a BCH address since the transaction is considered valid on both chains*. Resulting in merchants receiving more than what was intended.
*However, BCH saw the problem beforehand and implemented replay attack protection. They implemented this through the OP_Return (Making transactions with the message valid on Bitcoin Blockchain and invalid on BCH blockchain) and through a change in the signing mechanism. [1]
[1]https://github.com/Bitcoin-UAHF/spec/blob/master/replay-protected-sighash.md