Ether that you own (not related to the DAO) before the fork happens would be unaffected by the fork. But after the fork, suppose you accept payment for something. You can accept payment in cash, Bitcoin, Ether-on-left-side-of-fork, or Ether-on-right-side-of-fork. I suppose you could also insist on getting paid in BOTH "Ether-on-left-side-of-fork" and ALSO in "Ether-on-right-side-of-fork", but that starts to get really complicated.
In practice I think I'd sooner switch back to a non-forked cryptocurrency than try to deal with running multiple forks and ensuring that I'm getting paid on all of them. That sounds like a right huge mess to deal with, as you point out.
Not if the transactions happen after the fork, and on the "wrong" one. If you're purely using Ethereum as a store of value, and already have all your funds put into it, then this won't affect you, sure. But if you're actually trying to use it as a currency like intended, then you're screwed.
Money isn't very useful if you can't transact it at all for fear that new transactions won't be any good.
I assume he's being facetious, because it is confusing. Especially imagine someone requesting payment in Ethereum, and you think you've paid, and then they come back and say that you paid with funds on the wrong chain, and to re-send the funds on a different chain. There isn't a client I'm aware of that supports simultaneous operation on multiple chains. It gets very hard to deal with very quickly.