That depends. I'm active on several forums, most of which (including MacRumors) don't accept security keys, though about half of them do support TOTP codes - which I'd say are good enough. If a site doesn't support any 2FA whatsoever, then indeed, I will think twice about registering, though in most cases I will probably decide that the amount of knowledge I could gain from it is worth the trade-off. I'll just use a unique strong password and hope for the best. If that site gets hacked, I'll lose nothing.
Me too. I keep a secure note in my Keychain for that.
That's absolutely pointless. The whole point of 2FA is two add something you have (e.g. phone, laptop, Yubikey, whatever) to something you know (i.e. password). Using something you know as a second factor is a stupid idea. It's just like having one password which you are asked to split in half and to enter each half separately.
Whoever designs a website like that should quit working in IT and take up carpentry instead.
Of course, if you come across a website that's set up like that, then you have no other choice but to generate two strong passwords, one of which will be the password per se, and the other one the answer to the so-called "security" question, then to store both in your password manager. Frankly, in this case I would strongly consider whether that site is really worth registering on. I think this design would be an even stronger deterrent for me than the lack of support for physical keys is for you.