Hi Vikki, I'll give it a try.

Il se demandait si elle viendrait. That is indirect speech in past tense. The direct speech equivalent is: Il se demandait, "Est-ce qu'elle viendra?" You can see that the direct speech is in future tense. And future tense becomes conditional when the first part of the direct speech (il se demandait) is in past or imperfect tense. This is actually the same as in English: He wondered whether (if) she would come.

EDIT: I made a mistake in a reply to Thalia earlier in this thread and went back and fixed it. Sorry for the confusion.

The point is that "que" + subjunctive can be translated as "whether" in some limited contexts, as shown in the lesson. In English, "whether" can also be used to introduce an indirect question, but you can't use "que" + subjunctive in French, you have to use "si" + indicative instead.

I think "Je me demande qu’elle vienne" is incorrect.

I think it sounds fishy too. According to what I know, it is used in a whether..or kind of meaning:

whether you like it or not -- que cela te plaise ou non.

I'm a bit confused, Chris. Wasn't "Je me demande qu’elle vienne[t]" your own example?

(See your answer to Thalia in the Q&A for this lesson.)

If it was, then I made a mistake. I'll look it up.

In your revised answer to Thalia, "Je me demande qu’elle vienne ou pas." is still wrong, I think. 

Compare it to the example in the lesson: "Je me demande si tu vas venir ou pas."

"Que" + subjunctive has to mean "regardless", and in this case "whether ... or not" is an actual question.

EDIT - 

Maybe it's a little more complicated than I've suggested. In one of the examples, "whether" does not mean "regardless", although there is still a sense that the answer to the question is irrelevant.

La question n'est pas que tu l'aies fait ou non.

The question is not whether you did it or not.