Yes, it is assumed that mining will continue based just on transaction fees. In fact Bitcoin Core almost reached this goal recently due to their hard limit on block size, the percentage of fees in the total Bitcoin Core block reward reached as high as 40% according to the statistics: https://fork.lol/reward/feepct
So with the hard limit there's a set amount of transactions that fit into a block? And whoever wants to get their transaction validated faster can bid a higher fee?
Yes, that is why the transaction fee for BTC has increased in the past (see https://fork.lol/tx/fee), which some people didn't like and argued for a larger block size.
