Take it with a grain of salt cause I'm not native, but as far as my understanding goes the first two are not correct. The first is gramatically incorrect (maybe it is good in some context, but I don't know it), the second is technically correct, but weird, and the last is correct.
It's a double use of past tense. Normally you would say either "Have you gone there?" (which still sounds weird, because "gone" suggests someone hasn't returned; it would work better with another person) or "Did you go there?", depending on context. "Have you went there?" also sounds weird.
Have you ever gone there?
Is gramatically correct, but weird, because you would usually ask "Have you ever been there?". "Gone" suggests that someone went somewhere and hasn't returned, so asking if someone has ever (in a period of time, being their life) went somewhere and hasn't returned. So they went there and are still there, but the word "ever" doesn't work here, because it means they are talking after the fact ( I think? I got confused myself when explaining that, to be honest).
In short, asking "Have you ever gone there?" is like asking a person standing in front of you if they went somewhere and still remain at that place, which is logically impossible if we are talking to them at another place.
Though I think you can use that informally, just that it's not exactly correct logically.
That's absolutely correct (though it works better with "here", I think), and it's used to ask if someone visited someplace in general. It can usually be used instead of "Have you ever been there?", it's just more general, though it usually refers to a place someone is in at the moment, while "ever" suggests you're asking about some other place.
For example, "Have you been there/here?" can be used when you're standing in front of a museum and asking your girlfriend if she has been there, and "Have you ever been there?" is used if you are asking the same question at home.
"Have you been there?" also refers to more recent past, I think.
Edit: On second thought, I'm pretty sure the third one is not correct in formal English. Though I don't see problems using it informally.
Not sure how correct my take on it is cause I'm not native, but hope that helps.