That would be "театр здесь?" By including есть you're making the existence of the theatre the main point of the question. You're not sure that there is a theatre here and you want to find out if there is one. With "театр здесь?" the existence of the theatre isn't in question. You already know exists, so now you ask is it here or somewhere else. I hope that makes sense.
It is a coincidence. Basically, the same reason "eats" and "is" are sort of similar if you squint (isst and ist in German, though, sound exactly the same). If you are really interested, the first vowel used to differ for "to eat" but it merged into Е a few centuries ago. For the same reason, the Ukrainian verb for "eat" is "yisti" (in Ukrainian the extra vowel eventually changed into i, not into e).
- think of how "meat" and "meet" sound the same in modern English but were obviously pronounced differently when their spelling was conceived.
Есть is the infinitive for a verb "to eat", which has a rather odd conjugation:
- singular: я ем, ты ешь, он ест
- plural: мы едим, вы едите, они едят.
It is also the only available present-tense form of "to be" (быть). We mostly use it in structures that state existence, including the one meaning possession. The object that exists is the subject of the sentence:
- Есть одна проблема. = There is one problem.
- Здесь есть вода. = There is (some) water here.
- У меня есть вода. ~ I have water.
While I understand the reason why I missed this one, the translation suggested was "Is there the theater here?".
Perhaps this makes sense grammatically, but this is a semantic paradox. I mean, I can't ask if there is a theatre here if I already know that theatre. It only makes sense if I ask "Is there a theater here?"
Or maybe there is a more far-fetched situational context for "Is there the theater here?"