As Mikka explains, sidechains don't need to create their own currency, using bitcoins in the sidechain is precisely the point of two-way peg (there's no reason why an altchain with its own currency, like say litecoin or ethereum, couldn't support 2-way peg and also become a sidechain though).
Also, take into account there's several possible ways to implement sidechains. I will talk about the most basic one.
First some bitcoins are moved to a "pegging pool" for each sidechain and get locked there on a script until someone provides a scriptsig that satisfies some of them.
The user uses that "proof of suspension" to get the same quantity of btc in the sidechain. To prevent reorg risks, there must be a quieting period of X blocks in btc before the coins are accepted in the sidechain, say 100 bitcoin blocks.
After that, the coins can be send normally (or with the special rules the sidechain may have).
At some point, a new owner wants to move the bitcoins back to the main chain.
To do that he produces a "proof of burn/resumption" transaction (that needs to have a legacy format the bitcoin chain can understand). Then again there's a quieting period of X blocks in the sidechain before the coins can be claimed in the main chain.
To claim the coins back on the main chain, the user needs to provide the all the headers of the sidechain from the last time coins were withdrawn from the pegging pool to the block containing the resumption transaction (since this could easily become too long, even bigger than a whole bitcoin block, a compression mechanism is needed; I won't describe this but I'll just say that relies on "lucky blocks" and once implemented would be generally good for headers-first synchronization), the merkle path to that transaction, plus the additional X quieting blocks on top of it. This way we know how much work this chain has and that the transaction is included in that chain and buried with X blocks.
The bitcoin network doesn't need to know about the validity of the chain provided, only about the work. In that sense 2-way peg has a level of security equivalent to SPV because the chain with more work is trusted without fully validating it.
But as you say, how does the bitcoin network knows there's no other longer chain somewhere else?
It doesn't, so something else must be done to prevent sidechain miners from stealing the coins by just providing an invalid chain with enough work.
So, yes, we need yet another quieting period during which anybody can submit a "proof of reorg" with a chain longer (more work) than yours which doesn't contain your resumption transaction, invalidating your claim and making you start again.
So to steal coins an attacker must to control 51% or more of the sidechain's hashing power for the last quieting two quieting periods, the last of which could be set to days.
On the reward question, again, there's several possibilities. The simplest approach would be for the sidechain to live on transaction fees like bitcoin itself will have to do in the future. Another possibility is to distribute the fees between several future blocks to have a more predictable and constant reward. Another probably less popular approach is to have a demurrage fee on the bitcoins on the sidechain. I'm sure there will be more proposals.
You can read the original thread on 2-way peg here:
There have also been many discussions on #bitcoin-wizards :