It has different meanings. 1) be located. For example: Кинотеатр находится в центре города. The cinema is located in the city center. 2) to be (to stay) somewhere: Он не мог долго находиться дома. He couldn't be at home for long time. 3) to be in a particular state, condition: находиться под контролем - to be under the control

Находится literally means "finds itself' but can be used to mean "IS" in the sense of location (I heard there is something similar in some other European langauges). We don't have 'is'. But sometimes you Want to have a verb with "is" meaning. You can say Нью-Йорк в Америке. Нью-Йорк находится в Америке. Both mean: "New York is in America". The latter is more explicit, 'encyclopedic' style. It is also used in conversations when it is less clear from the context that it is _location_ that is questioned. The former (New York in America) sounds a bit ambiguous: i could be a part a something else, like "New York in America and Casablanca in Morocco are..." There are other meanings of 'находится', more literal ones. E.g. (1) "мяч нашёлся!" the-ball found-itslef! More or less the same as "The ball is found", or "we've found the ball". The context is that you lost a ball and were looking for it. Then someone found it. You could say "Я нашёл мяч" that would mean the same. But you make the ball the Actor here, as if it is the ball that let itslef be found. You do that to shift emphasis from "who found the ball" to the fact that the ball is back:) And it feels natural, because "finding" is always unexpected. It is out of your cotnrol, as if it was the ball who decides to be found. (2) figuratively У меня найдётся для тебя [job , a free evening, a sandwich] by-me will-find-itself for you [....]. A common indirect way to say, I have a job/time/sandwich for you. Sort of "no problem at finding it. If I search for it, I'll find some for sure". Mostly it implies asking: either you have already asked, or I say that in case you ask, I'll have some.

There are two meanings of the verb находиться. 1) (meaning mentioned in your words list ) imperfective pair (https://en.wikibooks.org/wiki/Russian/Verbal_Aspect) for the perfective verb найтись 'to be found'. The perfective form найтись is frequent, imperfective form находиться is quite rarely used. 2) to be located, to be somewhere. Eg: дом находится рядом с метро -- the house is (located) near the subway station. There are many possible translations of this verb, depending on the context. You can find some examples here: http://context.reverso.net/translation/russian-english/%D0%BD%D0%B0%D1%85%D0%BE%D0%B4%D0%B8%D1%82%D1%8C%D1%81%D1%8F

It means "to be somewhere". For example, "Он находится дома - he's at home"

It has a few meanings, you could say "Не найдется ли у вас? — Do you happen to have?" if you break it down "находить" (to find) + ся (itself), you get something along the lines of "will something find itself at your disposal". Он нашелся, что ответить. — He was quick to find an answer (here it means to find the right words to say) But I would say 80% of the time "находиться" is used to describe location, где здесь находиться банк? - Where is a bank around here, hope that helps