To raise/lower the blinds or to draw the blinds?

Solution 1:

"Raise/lower" would be correct. Instead of "pull", one tends to hear "put" instead. i.e. "put the blinds up", "put the blinds down".

Being British, I've only ever heard "draw" used when the curtains/blinds move sideways from the sides of the window to the middle, not with blinds that go up and down.

As for just turning the slats of Venetian blinds, that's tricky. I think if the blind was already down, but with the slats open, saying "close the blinds" or "close the slats" would be understood correctly, but maybe not if the blinds were up to start with.

Solution 2:

One of the meanings of draw is to pull (think of draft horses), so whichever way you are drawing curtains or blinds, open, closed, left, right, up, down, it is an acceptable usage. If you want to be more specific, you certainly can use a different verb (raise, lower, open, close, etc.)