You can do round/squares either way.
You could even do a tube with turning but it wouldn't be as easy if it was a small tube.
Stitches give a different look depending on if they're worked in the same direction or turned. Not turning also gives a right side/wrong side to the stitches.
The pattern should tell you if it wants you to continue in one direction or if it wants you to reverse directions.
I would assume if it doesn't say turn it doesn't want you to turn.
BTW, there's a crochet forum a little bit down the list.