Is there some sort of rule about how many sentences should be in a paragraph?? You would think I'd know being a uni student, but all my SERIOUS writing up until now has been academic, and I'm not sure if the same sort of rules apply?
It really depends on the style you're going for. In school I was told a paragraph was no less than four sentences for an essay, but they should really be more like five or six. In creative writing, though, it's different. You really need to focus on the ideas. A paragraph is merely a way to separate ideas. A paragraph should not contain more than one idea traditionally in essays. In creative writing it should focus on one character or idea. If you change characters, change paragraphs (especially in dialogue). While these guidelines can help with formatting, it's hard to just give a rule for paragraphs. It really depends on the needs of each individual piece.
In general, a paragraphs should not contain dialogue from more than one character, or dialogue directed toward different lsteners. Exceptions may be made for several very short speech fragments, but you should usually break paragraphs to separate speakers. A scene change should also begin a new paragraph. Other than that, what Lovely said is a good way to look at it.
No, there's no rule to say it has to be a particular length. It sound like you're just at the beginning stages, so just write without worry of anything at the moment. Whatever rules you've been told exists, put them to the back of your mind and just enjoy the creative side of writing. Like with your academic essays, editing will come in later.
absolutely not... there should be only as many as are needed and 'go together'... both lovely and cog have given good advice... follow it...
Another reason to break up a paragraph is to avoid a wall of text. It need not be a new idea, subject, change in pace, or anything that would normally need a new paragraph.