I'm an English learner and I'd like to know which verb should I use when using the word venetian blinds. Do you say 'to raise/lower the blinds' or 'to pull the blinds up/down?' or 'to draw the blinds'? + What would you say if you just wanted to turn the slats - would you say something like 'Close/open the blinds, please.'?
It would be understood in all variations that you proposed. However, "draw the blinds" only applies to closing/lowering, generally, not opening/raising.
If the blinds are vertical (from the top of the window) using raise/lower or pull up/down would both be correct.
If they are down and you want to adjust the slats I would use close/open. You may need to specify in that case, though, by saying "close/open the slats" rather than "close/open the blinds." This is something that even native English speakers have been known to get confused about at times!