I think it depends on if you trigger the Alternative Minimum Tax. The default is that you don't pay taxes on ISOs at execution time, but if you trigger AMT then suddenly you do pay taxes, it can be a lot of taxes, and you may have no way to sell the stock to get the cash to pay the taxes.

(Obvious you should talk to a tax professional rather than taking advice from a random stranger on the internet before taking any action.)

You don't have to unless you sell I think. Similar to real stocks you don't pay tax on stocks. You pay tax when you sell them.