I know Taraweeh prayer is done after the Isha/evening prayer, but how many rakats is it usually? What separates it from the tahajjud prayer, which is also done at night as well?
There are a few different opinions on the prescribed rakahs for Taraweh, but the most common opinion is of 20 rakahs.
In mosques they usually1 attempt to complete the whole Quran within the month of Ramadhan, so they recite a little more than a Juz (1/30th part) of the Quran each night. It may take a few hours depending on the speed of the reciter. People who don't offer the whole 20 rakahs usually leave after 8 or 12.