Nope, if you grip with your knees your heels come up and you go into a chair seat. This makes for imbalanced riding which most horses except for the trusty lesson ponies/horses uncomfortable and unsure of themselves which can either mean they slow down and are waiting for a proper aid or speed up and act nervous/frustrated because the aid is not correct and clear.
My trainer likes when our knees resting on the saddle (not gripping at all) as to allow us to use our calf and full leg for aids. She has a very German style, though! Hope this helped!
I highly suggest you don't! I've always been taught to turn my legs out, and NEVER grip with my knees. I think it really helps because then you are sitting down better which generally helps your riding and how your horse is going to react to your riding. It also makes it easier to stay on the horse if they spook, buck, rear, etc.
I don't. I've found gripping with your knees causes a whole host of problems. The knee is a pretty significant part of the "spring" system in your leg. It, and the ankle, absorb a lot of bounce from the horse and helps to keep you steady. Locking either one of those joints compromises that. Gripping with your knees also has an effect on the pelvis. It tilts you forward and a lot of the movement through the pelvis is lost.
We actually do a huge amount of movement in order to absorb the horse's movement. Those who look like they're sitting completely still are actually moving a lot. For lack of a better comparison, locking up part of your suspension system can affect the balance of the whole system.