In the most general, sidechains will use SPV Proofs to send satoshis from the regular Bitcoin chain to the sidechain, and allows the sidechain to eventually send the satoshis back to the main chain once the owner of said coin is finished utilizing the sidechain. While in the sidechain, the main chain knows nothing of whats happening to the coin, the sidechain is the one tracking who owns what at what time.
No, a side chain is simply any chain with an asset that supports some form of 2-way pegging against BTC. There is no reason that side chains have to use the SPV proof mechanism for accomplishing this peg, or merged mining for validation. These are simply aspects of one example implementation pathway that was presented as a proof of concept of how a side chain could be implemented. The design space is actually quite large, however.