(Light?) rust removal from chain
As long, as you can easily move the links of your chain, there's no problem. Just lube them and ride them, and they'll be fine. The movement will rub any rust from the critical places. You may need to work the chain for a while before the links become free, a creeping oil should help get the links moving again.

That said, there are two ways to ensure that a chain won't rust (as quickly as yours):


Make sure they are always well-lubed. A surface that's covered by oil is not covered by humid air, and cannot rust. May work well during storage, not so well when you actually use the bike.
Use chains with an anti-rust coating. I have quite good experiences with this, though the chains are a bit more expensive. I'm not sure how robust the anti-rust coating is against sliding through a front deraileur, though (I only ride IGH). In any case, I've never had a rust-proof chain go stiff.

Of course, anti-rust coated chains still like being kept well-lubed...