All true ;-) but it's a hearing exercise. If both answers were equally accepted you might not learn to listen to the slight difference in "ba" and "be" and maybe you might even miss the concept of "be"+"ha"="ba" but most likely we never would have had this discussion at all. So I think it is better this way.
Actually each sentence seems to be linked to several exercises. Sometimes you get audio somtimes not. Sometimes its hebrew to english, others its english to hebrew. I often get the same sentence multiple times in the same lesson just with different exercises. They alwats link to the same set of comments. Just because you got audio this time doesnt mean everyone always does. This why other words with same spelling but different pronunciation and meaning get the nikkud but for some reason they dont do this with the "be" and "ba" prefixes.
The verb תומך is used a lot more often in the abstract sense (support a party, support a family member) than in the physical sense (one thing leans on another); for the physical sense there are other verbs that are more commonly used.
In the physical sense, it's sometimes used as a direct object (העמוד תומך את הקיר), more commonly העמוד תומך בקיר. In the abstract senses, it's always with ב. It seems that in the bible both are used, but spoken Hebrew obviously prefers ב.
I understand what you mean but I don't find that example particularly useful. You revel in something because it's like (to me at least) basking IN it. The way you'd warmth of the sun. If you revel without the "in" you're having a raucous time! I am lectiophile but I don't know all the grammatical language they teach linguists and grammarians (I went to a kind of Fame high school & college, so no help there). However, https://www.usingenglish.com/reference/phrasal-verbs/ .
With that said, sigh... Does Hebrew treat prefixes the same way?
I've been asking around about this sentence, and here is what i found (hopefully it will help other people):
The preposition "ב" clearly doesn't ALWAYS works as "in the" does in English, and explaining it in a logical way is somewhat impossible. It is what it is, and every language has this kind of thing, so just learn where to put it and deal with it.
This sentence states that "we" give "abstract support" TO animals in general (like a pro-animal organization, and not like holding literal animals on your literal shoulders).
Although it WOULD make "logical sense" to say "אנחנו תומכים את החיות", it is grammatically WRONG (meaning a native Hebrew giggle and deal with your mistake much like anyone deals with people that are not native in our language). So just learn that "to support (smth)" is "לתמוך ב". Learn them together; not apart.
What really gives the direction of the "support" is the verb. " לתמוך ב" is to support whatever comes next; "להיתמך ב" is to be supported by what comes next.
There is also the preposition "על", that, at this point, we did not learn yet.
There's actually some generalization to your last examples. Another general meaning to the preposition ב, in addition to "spatially contained" and "temporally contained", is "using (an instrument), for which English generally uses "with". Indeed, in your three examples English wouldn't use "with", but it may seem less strange - "watch with TV", "use with phone", "use with toilet".