Learn German: Wir haben eine ganze Weile gewartet.

In German, time expressions that describe a duration (how long something takes) without a preposition take the accusative case. Here, eine ganze Weile tells us exactly how long the waiting lasted.

English uses "for" in "waited for quite a while". Why isn't there a translation for it (like für) in the German sentence?

While you might occasionally hear für used for durations, the standard and most natural way to express "for [a period of time]" in German is simply to use the plain accusative case. Using für is usually reserved for intended future durations, like going on a trip "for a week".

Does ganze literally mean "whole" here?

Literally, yes ("a whole while"), but idiomatically it translates to "quite a" or "a good". Adding ganz or ganze is a common way to emphasize that a duration, amount, or distance is surprisingly or significantly large, just like saying "a good while" in English.

Since this lesson is about words like inzwischen (meanwhile), where would I put it if I wanted to add it to this sentence?

You have two natural options. You can put it at the very beginning (Position 1), which forces the subject after the verb to maintain V2 word order: Inzwischen haben wir eine ganze Weile gewartet. Alternatively, you can put it right after the conjugated verb: Wir haben inzwischen eine ganze Weile gewartet.