Once all the bitcoins have been mined, it’s supply would be tapped out. Then as you said, the miners will get incentivized for processing transactions with fees.
This will be the case. Miners will be compensated for confirming transactions in the block. But I do think that the closer we get in reaching the 21 million supply, the lower the denominations would be in mining. Obviously, price of BTC would skyrocket when that happens (Law of demand and supply) but a fork might be needed in order the 21 million supply to somehow be affected.
A hard fork that would increase the coin supply.
There's no reason to ever increase the coin supply. Not-even-one. The system works currently with
this circulating supply and any change in it would be consensus-ly irrational.
As I said before, there'll never be a user who'll support this because it'll instantly reduce their wealth power. One may fork the code and increase the supply; no one will follow other than those who aren't using Bitcoin and want to have profit.
While a hard fork might be the answer, I do agree that it is not needed as the system works as it is. The volatility might also change thus disrupting the market price.