"except for" vs "other than"

Solution 1:

In your first set of sentences, except as a preposition means "with the exclusion of; excluding." So, in your example, you would be saying "Are there any vegetables excluding asparagus?" This is incorrect because you are not excluding asparagus; you're actually wanting to know if, in addition to asparagus, there are any other vegetables. You're including aspargus as a vegetable, not excluding it.

In your second sentence, other than means "different from or besides." It is correct. In fact, you could correctly say, "Are there any vegetables besides asparagus?"

Your last set of sentences have the same meaning: I love vegetables in general, but not asparagus. In those sentences, except for means "but for" and other than means "besides."

Solution 2:

I think what's wrong is the "for".

Are there any vegetables except asparagus?

The grammar of when to use "except for" and when to use "except" is governed by a quite complex set of rules (often, you can use either). There probably is a correct and complete description of how this works somewhere on the internet, but I haven't found it, so I can't tell you why you should use "except" here; but it just feels right.

Solution 3:

You're correct in that the first example is wrong, and that it's hard to nail down exactly why. The two phrases are quite similar, and in your second case neither is incorrect. Perhaps, though, other equivalent phrases can highlight the difference in usage if you replace