Your frustration is understandable, and I think a lot of players go through this at some point!
Here is one way to think about it which avoids having to imagine a hypothetical board:
Pretend that the ko rule doesn’t apply to one of the players!
In your first problem, if the ko rule doesn’t apply to white, then white could take back at T2 immediately, and the black group will die. So black should look for a better variation.
In your last problem, if the ko rule doesn’t apply to black, then black could take back at T2 immediately, and the white group will die. So this variation is better for black than the one where white lives unconditionally.
This approach is used by the problem site sahwal.com (it’s not well maintained, but if you bypass the security warning it seems working again at the moment - it’s been completely unavailable for a while), where ko is never the solution. There it’s assumed that the opponent can win any ko, so if you take a ko, the computer takes back immediately.
Now this “trick” doesn’t help in distinguishing between differently favorable kos (who takes the ko first etc), but it works to distinguish between the basic life/ko/death cases.
(I’m not saying this is a better way of explaining it than referring to a real game situation, this is probably more confusing to a lot of people. But I’m sharing it just in case it’s a helpful perspective to someone.)
It doesn’t! It just doesn’t have problems like that. It’s either possible to live outright or kill outright.
It’s a different convention than what we’re used to. Since they have automatically generated problems and want the computer to be able to answer every move you make, they have to use rock solid rules to avoid having ambiguities like “is ko or seki better?” (which as @Vsotvep mentioned, can’t really be determined in isolation)
A side-effect is that it’s (IMO) easier to understand for new players.
Of course many kinds of nice problems are not possible in this setting, so it’s not like everyone should switch to this other convention. But as the site demonstrates, there are thousands of possible problems, even under the very strict limitations they’re working within. (apart from the ko thing, every position is aways completely enclosed by a solid chain without cutting points, and only life/death matters, never territory/points)
Interesting idea. So it’s basically saying “let’s not worry about how to make use of a ko at this point.” But I’m unsure if it’s easier to learn that at a later point.