If BTC really dominates our world, will 2.1 quadrillion satoshis be enough for the blockchain functionality to run other applications?
Probably. If not, then either the program will be changed to allow smaller increments (nano-bitcoins? pico-bitcoins?), or services will be created for off-chain transactions. (I'm not sure, but I think that the new side-chain concept that SegWit makes possible might also be a solution?)
What will happen when limit approaches?
What limit?