Do clipless pedals make that much of a difference?

[OakLeaf]

Does clipless help or worsen patellofemoral syndrome (runner's knee)?

Helps, as long as your cleats are aligned properly. With toe clips and no cleats (I don't think you can even buy the cleats for toe clips any more???), your feet will position themselves according to the shape of your shoes, which may be very wrong for your knees. Alignment is critical, and if you have no cleats, you can't align your feet.

Does using the clipless pedals make you much faster right away? What muscles end up getting worked out?

Cycling shoes make you faster right away, because of the stiff sole. When I got my first pair of cycling shoes 25 years ago, it was good for 1.5 mph. As I said, AFAIK you can't even buy toe clip cleats for cycling shoes any more, so nowadays going to cycling shoes automatically means going to clipless pedals. You'll find you use the backs of your legs more, hammies and calves, and also your hip flexors to pull up when you stand to climb, rather than just mashing down with your quads.