I read here that "The interests for the current month (Direct Interests = on your balance + Referral Interests = on godchildren) are calculated on the last day of the month at midnight (and not on the run of the river) and are then added to your current balance."
Does this also mean that the Direct interests on my invest automatically are compounded, without anything having to do?

Indeed, you don't have to do anything on your side: the interests (Direct Interests = from your balance + Referral Interests = on godchildren) are automatically added to your balance at the end of the month and the whole is immediately reinvested.