I can speak to the first issue only:
A side position might put weight, stress, or unusual extension on nerve, muscle, or connective tissue that hasn't healed sufficiently. If you really like sleeping on your side, try this in the daytime when you are awake (!) and have some time for bed experiments (no snotty comments from others, please).
Lie in bed on your side with the operated leg on top. Lie there until the pain only just starts. Try to rule out lower back tension/swelling/strain/ by pulling your knees a couple of inches closer to your chest (this bends the legs more and straightens and eases the lower back). lower back tension (and tight hamstrings) can trigger sciatica and likely other referred (i.e, you feel it some distance from the source) nerve pains.
Also try resolving the Downhill position of the top leg (as seen from hip bone to ankle), as stretching the leg over the hip (or incision site) might cause pain and that sleepless aching -so please try putting a pillow between your thighs and extend it to between your feet - or put a second pillow between your ankles and feet. (one or two pillows depends on length of pillow, pillow size, your size, and how much you bend your legs). Sometimes the "top" leg wants to be parallel to the mattress and not squished over. Or the bottom leg doesn't want to be squished by the bony knee of the top leg. the point here is to "shorten" the stretch between your waist and that knee along where the outer seam of your jeans would be...
We forget how wide the pelvis is (especially for women) and side-sleeping requires one leg to whack way over, especially if you cross the top leg above the bottom leg. Sideways weight also pushes the implant into the socket in a loose and non-weight-bearing way. If you discover the distinction between a painful and non-painful position tell your PT and they can likely tell you the source. If you can not identify the problem then do ask your PT about it, and work with them on side positions!
BTW I could not sleep on the operated side for quite a while, but could manage a semi-side/back position by putting pillow behind my torso and kind of reclining a bit towards it.
Either way this will ease over time but it is more interesting (and useful) to investigate your difficulties and work with your body position when you are alert and awake. Good luck, I'm a huge fan of sleeping for health!