This is an idiomatic construction using (verb + da + a period of time). For example, "aspetto da agosto" or "aspetto da molto tempo" would mean "I have been waiting since August" or "I have been waiting for a long time" respectively. It is definitely confusing because the "da" doesn't just change the sense of the phrase; it changes the entire meaning (as well as the tense). Its just one of those things you have to memorize and watch out for.
Way better than perfect. Uhm, as far as I remember, Duolingo serves for the purpose of "teaching languages" and it really does that with the leveling system for the lessons, putting bricks one by one, moving forward from basics to something more difficult, gradually.
So, yes, that'd be great if they teach me how to use the present perfect continuous tense, before asking me to translate it, just like how they succesfully do that in the other lessons up to now.
I cannot disagree more. Duolingo teaches you the brick by brick method and simultaneously shows you expressions which might have easier construction in Italian than in English. In that sense it doesn't ask for any translation of present perfect continuous, since "aspetto" is nothing more but present simple. It shows you that present simple can be used in various situations, in case you want to know them and I find that advantageous.
A good question! I have no idea how the literal translation would go over to a native speaker, but "I can't wait for August" would be "Non posso aspettare per Agosto." However, when in doubt, change your wording. "I'm excited for August" would be a sentence that both languages would accept.
"I have been waiting" is in the present perfect tense, or more precisely, the present perfect continuous (aka the present perfect progressive). Actions described in the present perfect have some connection to the present.
In this case, "I have been waiting since August", and I am still waiting.
No, that is the direct translation. A more appropriate translation is "I am waiting since august." The best translation (the one that delivers the closest meaning in English) is "I have been waiting since August." Direct translations between Romance languages and English are good only about half the time.