You can always use zbyt, and you can use za only before many, but not all adjectives.
You cannot use za-adverb after za-preposition (za za would look and sound silly).
You cannot use za before participles.
You cannot use za before negated adjectives.
copied from @vytah https://www.duolingo.com/comment/13082422
It's tricky to try to translate literally from one language to another. I've spoken both languages all my life and I really "think" and perceive differently in each one. So for me (and just me and not official grammar books) za krotka means too short and zbyt kroka mean a bit short (that is, not quite "too short")
Jellei, would you be able to explain the difference between "zbyt" and "za"? I am still confused after reading all the comments. Immery says that you can always use zbyt. But, I think it might change the meaning. For example-- "To jest zbyt dużo." "To jest za dużo." My Polish is not very good, but I would take the first to mean, "That's too big," and the second to mean, "That's too much." Is this accurate? (Like, if you handed me $30, and I wanted to tell you this is too much money.) How do we know when to use which?
On the level of this course, it seems safe to consider them perfectly interchangeable. The rules aren't exactly set, that's more a case of what is a more common collocation. Professor Bańko says that "zbyt" is always safe, but "za" sometimes doesn't work (for adjectives derived from verbs and for adjectives starting with nie-), but that's some advanced stuff anyway.
No, in those sentences za/zbyt doesn't change anything, it's what follows them that could change it. You used the adverb "dużo" in both cases, so it refers to the amount: That's too much. In order to mean "That's too big" it would need the neuter adjective: "To jest [za/zbyt] duże".