"inter" means "between" or "among".
"between" is used with two; e.g., the letter B is between A and C.
"among" is used with more than two; e.g., I'm among Tom, Bob, and Linda.
Technically you're right, yes, but it's very common to hear "between" with three or four things.
In any case though, "inter" works in Esperanto for both cases.
Yes. Anyway, searching about "between vs among" gives some rules to choose between "between" and "among", the simplest one of them is the mentioned :)
To me, between means that you are in the space between other things (doesn't matter how many) while among means that you are generally around.
You're right. This is the same as you are between two groups of it; e.g, I go between trees = I go between two groups of trees. :)
In almost two decades, I've never been troubled - or even noticed - that "inter" has "two meanings." Is it perhaps a case of it meaning "between" when there are two and "among" when there are three? This is more a question about (my native) English, I suppose. Is it possible to be "among two trees" or "between three friends."? I don't think so.