Here is an example:
He wondered who stole his television and why a calling card was left behind.
Do I need to separate the two clauses (e.g. with a comma between 'television' and 'and')?
Any advice is welcome.
From most of the examples in this link, keeping or omitting a comma would suffice.
Also, it could be said that the latter clause (and why a calling card was left behind) is a dependent clause, thus it would be best to omit the comma.
Not really. Not two clauses.
Now three clauses would have to be:
He wondered who stole his television, why a calling card was left behind, and whether this was just the beginning of a long chain of events.
I hope this helps.
Some people feel very strongly about "correct" punctuation, while at the other extreme some will argue that punctuation simply provides useful signposts to the reader and there shouldn't be too many hard rules. To some extent punctuation is a matter of style, so it's worth checking if there's a style manual you're expected to comply with.
It's common practice for clauses that share the same subject not to take a comma before "and", whereas clauses with different subjects do take a comma. In your example, the common subject in both clauses is "he", so a comma isn't needed.
However, commas are also a signpost for the reader to pause, and in some situations you may want this to occur even when a comma isn't required - for instance, to create a dramatic effect or to help with the flow of a long sentence. Inserting a comma in your sentence subtly changes it: the pause gives the word "why" a very slight emphasis. If this is important, add the comma; if it's not important, leave it out!