Is it possible to add "goers" at the end of any word (words indicating a place)? I know there exists the words like: restaurant-goers, church-goers, etc. but I'm not sure about the other words such as hospital, or bank.
What about the hyphen? I mean the usage of the hyphen between the word and the "goer(s)", is it arbitrary?
The Free Dictionary lists fairgoer, playgoer, filmgoer, beachgoer, operagoer, partygoer, moviegoer, cinemagoer, churchgoer, gallerygoer, concertgoer, theatergoer (/theatregoer) and festivalgoer (but not your example of restaurant-goers). All of these are leisure/pleasure activities which people have some sort of choice about. Almost everyone does these activities at some time or another, but these 'goers' do it especially often.
People 'go' to hospitals (as a patient or visitor) and banks, but those activities aren't really leisure/pleasure activities with some sort of choice. If you said you are a 'restaurant-goer' I would understand what you mean, but if you said you are a 'bankgoer' I wouldn't, and I'd have to ask you what you mean.
This answer addresses the hyphenation question, as Sydney has covered the first element of the question.
All punctuation is arbitrary, even if there is broad agreement on when it should be used, but I interpret your question as
Am I supposed to use the hyphen when adding "goer" after a word?
The answer to that will vary a bit from case to case, as using "goer" as a suffix isn't really a part of English grammar by itself. A hyphen usually connects words that would not obviously be connected when reading a sentence. The "obviously connected" part can be subjective: printing press is a common enough phrase that casual readers will recognize it as a compound noun even though is is an open compound (two distinct words, not connected with a hyphen).
When an open compound form of a noun would not necessarily be obvious to readers, a hyphenated compound is a way to show that the words are meant to be interpreted together. That's the case with the hyphenated examples, helping to mark the difference between
At a party goers request a bartender will serve drinks
At a party-goers' request, a bartender will serve drinks
I added some extra punctuation, the apostrophe and the comma, to make the meaning of the second sentence overall clearer, but the hyphen clearly indicates that party and goer are linked and intended to interpreted together. The sentence could still be interpreted correctly without much trouble even if the hyphen were not used, especially with the extra punctuation, but the hyphen makes the compound phrase clearer.
Finally, closed compounds are both words combined with no space between them. Many terms which begin as open compounds or hyphenated compounds eventually become closed compounds, though not all. Many of the compounds that use goer have dictionary entries showing the closed compound, such as partygoer.
In general, I suggest that you follow the style you've seen used in native English writing. That's a pretty reliable guide to what a contemporary reader will recognize easily.
It's unlikely that anyone will be very confused by any of party goer, party-goer, or partygoer. But if you are adding goer to a compound phrase you haven't seen before I strongly recommend that you use the hyphen. In the case of a compound noun that isn't common in English, an open compound may be confusing (bank goer is not a phrase that is common, and so is not immediately recognizable) and a closed compound may look as though you're trying to use a word that doesn't exist.
The explicit connection of two words meant to be interpreted together, but not necessarily related in a way that would be immediately obvious to a reader, is what a hyphenated compound is for.