Can 걸까요 be put under every kind of sentence to make it a question?
Is it like the rising intonation that we use at the end of the sentence to denote that it's a question?
For e.g. in 여기에 걸까요, we simply add 걸까요 to 여기 to make it a question?
Another example 곰이 있는 means "there is a bear" and we add 걸까요 to make is 곰이 있는 걸까요? -> "there is a bear?"
Is this only used in spoken korean?
First things first: "여기에 걸까요" is a very different example. Here 걸까요 is a question form of the verb 걸다 (hang), so the sentence means "Shall I hang [this] here?"
If you want to ask "is it here?", then remember that the original sentence form is "여기다" (it is here): 여기 (here) + -이다 (be). So you have to say "여기인 걸까요?"
Normally, 걸까요 is short for 것일까요, that is, 것 (thing, fact) + -이(다) ("be") + -ㄹ까요 (making the sentence a question). So, it can be considered a question form of "거예요" (것 + -이에요).
곰이 있어요. = There's a bear. (Literally, a bear exists.)
곰이 있는 것이에요/거예요. = (The fact is that) there is a bear. (More emphatic and dramatic.)
곰이 있는 걸까요? = Is it true that there is a bear? / Do you think there's a bear?
Compared to plain "곰이 있어요?", -걸까요 form sounds more like story-telling, or curious situations. As if you're walking in a mountain and find a huge ominous footprint, and you say "...Do you think there might be a bear?"
In some situations, -ㄹ까요 can be considered a bit feminine, but these days both genders do use the expression frequently. You could find it even in TV news. Published materials normally don't use "해요체" (that is, -해요, -일까요, -이에요, and so on), so you will normally not find 걸까요 in text, except for children's book.
