Piano, carpet, area rug, hardwood: impulsive decision--now what?

Last night, in anticipation of having Coit in today, we managed to wiggle the (inherited) upright piano off the carpet in the living room (uninstalled 12×12 laid down on top of hardwood and essentially used as an area rug) and take a good look at it, underside and all. This resulted in a snap decision to roll it up and heave it out instead of having it cleaned.

What I’ve been wanting to do anyway, now that the kids are through spilling Cocoa Puffs in front of the TV and the incontinent cat is gone, is replace the carpet with a smaller centered area rug and expose more of the hardwood.

My questions:

— Is it all right to let the piano sit on the hardwood? Do I have to put something under it to protect the floor? I’m not expecting it to move around very much. (But of course the bench will move.)

— I love the look of these rugs (despite the odd spelling of karma) but don’t know the implications of synthetic vs. natural wool, especially on hardwood. Any advice for me?

— Is padding mandatory?
If yes, won’t there be a problem with the height difference? Will we trip over it all the time?
If no, what keeps the rug from slipping underfoot, and will whatever prevents slippage harm the hardwood?