I stand on short hills, on the steeper parts of long climbs, and on anything that's over 15% or so. Sometimes I stand just to use different muscles. If your knees are hurting when you stand it may be because you're doing more climbing or more standing and are overusing the muscles. On which case if you moderate how much you increase your standing, they should get used to it and you'll be fine. Weight lifting (squats, leg curls) can help.

My cadence varies from 65-75 on climbs to over 110 in a pack on the flat. When climbing, lower cadence puts more stress on the leg muscles (they are doing the same work with fewer contractions) but less stress on the cardiovascular system. Spinning stresses the legs less since the muscles do the same work with more contractions but since humans are not 100% efficient, there is more stress on the cardiovascular. So if your legs hurt but your lungs are fine, shift to a lower gear. If your lungs are burning or you are out of breath and your legs are fine, use a higher gear.

I've been riding no hands since I was a kid. It's easiest to learn on flat or slightly uphill, so you can pedal with some resistance. It's easier at speed (above 15mph or so), since the bike is more stable. Ride with one hand and try not to use the hand to steer the bike. When you're riding no hands you steer with your hips- shifting them causes the bike to turn. It's a slower way to steer, so you have to look and think farther ahead. And you can't make a sharp or sudden turn, gradual turns only, at least until you have a lot of practice. It'll seem impossible until you "get it", then you'll be wondering how it took so long to figure it out.