Hello,
I am about to install 1/2" plywood over 5/8" subfloor and I have a few questions. Does the direction of the 1/2" plywood matter (Length of the plywood perpendicular or parrallel to the joists) and does the joints have to land on top of the joists or can they be anywhere? Thank you for your expertise.

I usually put it the opposite way the existing plywood is installed. and edges of plywood on top of joists.

This does not matter as much under wood floors but when I tile I have to run the underlayment the same direction as the subflooring... just offset and staggered. That is the strongest way to do it, so I do them them all that way now.

Make sure to flatten out and re secure the original subfloor first. Keep an 1/8" gap around each sheet of UL and don't fret about hitting the joist.