Unless there's a pre-existing condition requiring it, I wouldn't wrap (and if there was a knee condition, I'd at least consider an over-the-counter knee brace as a more convenient alternative.)

Better "preventive" measures are to wear hiking shoes or boots (as opposed to running shoes, tennis shoes, or work boots) and/or to use trekking poles, in my opinion. Both reduce the chances of slipping or other injuries, and the poles reduce the pounding your knees take.

Putting your feet up (not necessarily above your head, which seems a bit radical) does feel good at the end of the day, but I really couldn't say whether it does any measurable good. It can't hurt!