Interesting what will happen with blockchain when all bitcoins will be mined. Transactions between bitcoin wallets won't work?
It's obvious that they will. First of all, this will only happen in 2140 (nobody here will be alive, so don't worry too much about it).
Instead of getting paid with the block rewards + mining fees as an incentive to keep mining, they will get only get paid with the mining fees, which should be enough (we hope so).