Actually, it doesn't matter at all what size they are, but it's recommended they be powers of 2. (So 2x2, 4x4, 8x8, 16x16, 32x32, 64x64 and so on)
Oooops, sorry, my bad. Powers of 2 it is. I've just made sure its powers of 8, and have had no problems, but ofcourse, any power of 8 is also a power of 2

1. Thank you) If I understood correctly, I can use rectangular textures, not necessarily square?
Yes. Sprites and other graphical elements can be rectangles, they do not need to be squares.
opefully able to explain.
Uhm, it's still a bit cryptic. If I understand correctly, you'd like to use a sprite to procedurally draw a line from X to Y. And then draw another similar line, but have a collision test so that the program knows if the latter line cross the former line? Like in a Tron-style lights-bike game, or Snakes for that matter?
There is no actual drawing commands in AppGameKit, so you'd need to make your own, where you clone a given sprite as many times as necessary to reach from X to Y and place the clones along the line.
As for checking if two lines meet, you could either use the built in collision commands, which check to see if two sprites collide. In a Snakes/Light-Cycle game I'd rather use a 2D array to represent occupied tiles/pixels of the play-area. The array method makes such simple collision testing non-iterative thus saving a lot of CPU time.