#1
What are some other power chord sounding chord shapes? I know on the E and A like the 133 type shape and 1x3 shape but I've seen some other guitarist use other shapes that sound pretty similar to a power chord to change it up.
#2
A power is a single type of chord (specifically, a root, a fifth, and an optional octave). That's all it is. The second thing you mentioned I'm guessing is an octave diad (a root and its octave).

If you want to learn more chord shapes, learn some about chord construction. Musictheory.net is really good for learning the basics of theory.
#3
x103xx letting the middle string play open. x13300, x52xxx(54/55), 547xxx, 759xxx, 35x4xx, x255xx, x055xx, 0022xx, 2244xx, 3355xx, 332xxx, 553xxx, 775xxx.......