How are the former miners being rewarded and is Bitcoin going to be more valuable by then?
Supply will stabilize, which should have a positive impact on price. What supply is constant the increasing demand will have a greater pull on the price.
As for the miners, transaction fees will start to encompass more and more of their earning from serving in a mining role. We'll also probably see more consolidation of the miners because the prospect of earning coins straight out of the blockchain won't pull in the independent miners as it does today.
It'll take a long time for all coins to be mined - the current estimate is the year 2140. However the block rewards will drop to very low numbers very quickly. The block reward halves (currently at 12.5 bitcoin per reward) after a pre-set amount of blocks have been processed (right now the pace is about 5 years between halving events). So within 15-20 years the block reward will be down to 1.875 Bitcoin. At that point there will be little incentive for independent miners to get involved, unless the price of a bitocoin goes up tens of thousands of dollars.