Now let's say there's a sidechain to this mainchain, which is trying out some new tech, let's call it thimblejimble. Now this thimblejimble sidechain tokens are valued at : 1 mainchain token = 10 thimblejimble tokens. First question: Does this statement even make sense? Do sidechains have their own traded tokens such that this is what the exchange would be like?
Well, this can easily be done by a centralized approach - buy 1 bitcoin and (provably) use it to back your new "pegged" currency by issuing 10 thimblejimble tokens.
So, from what I understand, to control 10 tokens in the thimblejimble chain, you would lock up one main chain token. I guess this means you leaving your private keys that control the main chain token behind, and somehow acquiring the private keys to 10 sidechain tokens? And then you transact in the thimblejimble sidechain for awhile with these 10 tokens (because that's what you do in a blockchain - transact (rearrangement of UTXOs and their private keys) - right? or am I not understanding what is going on within a sidechain's blocks?)
It's implementation dependent. One approach would be to allow new "partners" to join your pegged coin by putting their coins into a multisig address that is locked by their own signature plus the signatures of all other current partners who are backing the pegged coin. Suppose Dave wants to join thimblejimble as a backing partner - he plans to invest 1 bitcoin and receive 10 thimblejimbles of his own (the private key for the wallet containing 10 thimblejimbles). However, the coin is currently already backed by partners Alice, Bob and Charlie. So, Dave must lock up his bitcoin in a multisig address with Alice, Bob and Charlie as co-signers - the address is also hashlocked to permit an XCAT (cross-chain atomic transfer) when leaving thimblejimble. Once he has done this, they will sign a transaction on the thimblejimble chain authorizing the creation of 10 new thimblejimbles and assigning them to an address that Dave controls. When Dave later wants to cash out, he's going to need to show Alice, Bob and Charlie that he controls 10 thimblejimbles. They will then prepare a multisig contract that transfers Dave's 1 bitcoin back to him. Once he publishes this multisig transaction, along with the hashlock to unlock it, his thimblejimble address (which contains 10 thimblejimbles) will be unlocked (by the same hashlock) and destroyed on the thimblejimble blockchain.
Are you able to transfer the 5 sidechain tokens for 0.5 mainchain token?
With determination, I'm sure you could craft a system that allows partial exchange-out.
What happened to the other 0.5 mainchain token value?
You could prepare a transaction that unlocks all 1 of the mainchain token but then re-locks the 0.5 that is staying with thimblejimble back under a multisig just like the original:
[1.0] {Alice,Bob,Charlie,Dave} -->
-------
[0.5] --> Dave
[0.5] --> {Alice,Bob,Charlie,Dave}
what if the relative value of the chains change in these 2 months?
This should be impossible unless the sidechain experiences a major technical problem, resulting in breakdown of the sidechain's network (e.g. a major security flaw). In other words, 10 thimblejimbles should always trade for exactly 1 bitcoin (minus tx fees).
Can someone shed some light somewhere?
Take a look at this
this. It covers some of the history of commodity-backed (or "specie-backed") banknotes. The metaphor is that gold is like Bitcoin, while the paper banknotes are like sidechain notes. Ideally, you issue just one sidechain note for each Bitcoin and don't issue additional coins to try to enrich yourself.