- Мы ждём маму. = We are waiting for Mom.
- Мы ждём конца месяца. = We are waiting for the end of the month.
- Мы ждём зимы. = We are waiting for winter.
- Всё ждут судью. = Everyone is waiting for the judge
- Я жду автобус / автобуса. = I am waiting for the/a bus.
- Я жду письмо / письма. = I am waiting for the/a message.
Note that animate plural and consonant-ending masuline nouns have the same Genitive and Accusative. You do not even have to think when you use one of them (e.g., Мы ждём учителя/директора/детей/друзей/судей)
It’s not accusative. «Ждать» can accept both accusative and genitive.
It's not clear to me when you say "waited", "was waiting", "has waited", has been waiting" etc. as translations of these verbs in past tense. Sometimes I use one form and am marked wrong, but other times that is the accepted translation. Is there a rule for this? Here I said, "she has been waiting for an answer", and the computer didn't accept my translation. Was I wrong?
No, it works here, even though it is not the most obvious interpretation. If you state the amount of time, however, Russian normally uses the present form of the verb («Я жду тебя уже два часа»). Otherwise it would mean you refer to doing the action that long in the past (for an imperfective verb, of course).
Well. For starters, can you explain what is the exact meaning of "for" in "wait for something"? :)
For example, in "I worked for money" or "I bought this gown for $30" the word "for" expresses the idea of exchange, i.e. the action in question was paid for by the thing marked with "for". This is a typical situation for Russian за+Accusative.
In "This letter is not for me" the word expressed some directionality, the person getting some "benefit" intended by the one who performs the action (in Russian, we do not use для here all that often.)
Long story short, Russian ждать behaves more like English "await" or "expect"—I mean, grammar-wise.