Firstly, Bitcoin has no dependency on sidechains.  They are irrelevant (with some of the potential 'whale' effects that I've previously outlined.)

As for tokens, one potential implementation would be that they would be issued for Bitcoin pegs and redeemed in the same way.  The system would prove the circulation.  The sidechain back-end would serve mainly as an 'assay' agent which would make sure that the token was not bogus.  Probably transactions would normally involve having the tokens re-issued as a way to extinguish any previous claim after a transaction (which would probably involve a layered system of digital signatures.)  A nicety would be that they could probably be used 'off-line' in situations where one could at least temporarily trust the seller to be somewhat honest for a time and not be creating and issuing bogus tokens.  In the real world many transactions are done between parties who know one another and/or have reputations to promote, so for small sum transactions this would actually work quite well.

As I understand things, NXT is (in addition to probably being a scam) a token based system that (in theory) relies on 'proof of stake'.  A Bitcoin-backed token-flavored sidechain would not need 'POS' since it's backing is native Bitcoin.

Since you are so amazingly thick, let me again stress that this is but one in an infinite set of potential implementations for sidechains.  Most or all sidechains would need an interface layer where they interact with Bitcoin, and usually (if not always) support Bitcoin through the same old POW sha256 hash mining mechanism which, as I've also previously outlined, is conceptually economically broken as an enduring method of system support in a stand-alone ecosystem.