Hi there. To address a couple of your questions, I too have been told to get antibiotics before any dental work (even cleaning), and any other invasive procedures, as a proactive way to prevent any infection issues.
As for compression stockings, I'm 48 and had a partial knee replacement, and I wore the compression stockings for the few days I was in the hospital, but was able to remove them after that. I put them on occasionally for the next couple days when my legs ached (they felt good) but I had no Dr. instruction to wear them a certain length of time.
My understanding is that there isn't really anything that can help the scar heal, but for a gentle massage, light mineral oil can work, and I've heard others using Vitamin E oil - getting the capsules and breaking them open to access the oil.
I'm 8 weeks post op and have some remaining Vicoden I take sometimes at night for pain to help reduce the pain when I need to sleep, but otherwise I take Advil or Aleve during the day. My Dr. isn't filling prescriptions anymore for me at this point.
Everyone is different in how they handle weaning from meds, but I know slow and steady is the best way, and not to stop if you still have pain, as that will slow your progress with strengthening and ROM.
Best of luck to you!