I don't think it's a hard and fast rule, but when I was typesetting a reference book of song details, I was instructed by the editor:

(i) if the song title was actually the first line of the song (or the first part of the first line), then capitalise the first letter and leave it at that. Punctuation only where essential: from memory, there were a few question marks, but nothing else, e.g. no full stops at the end of the titles.

(ii) if the title was unconnected, capitalise the first letter, plus the important words (nouns, adjectives etc) but not the minor ones (articles, conjunctions etc). Again, punctuation only where essential.

This was in the UK, incidentally.

Definitely no spaces before commas, colons etc. I think I read somewhere that adding extra spaces was an old (and now also old-fashioned) convention of the printing press, adopted for ease of reading the printed word. I recall that Penguin books always used to use a space before colons and semicolons, though not before commas.

Within the body of the song, if the text is by a known author or taken a printed source, it's courteous and correct to follow the source material. For verses from oral tradition, the amount of puncuation is down to personal preference. I'm old enough to capitalise the first letter of each line of verse out of habit, for example, but otherwise I prefer to keep punctuation to the minimum necessary for clarity. The lines of verse give a natural break anyway, reducing the need for commas in particular, whilst, to my mind, using a lot of punctuation makes for fussy breaks in the flow of the text.