I. If it is a flat style motion graphics I would not use JPG (Or any compressed video format) to prepare an animated gif. Use PNG.
The reason is that there is a chance, due the JPG compression, that flat color areas create some compression artifacts, which basically is a slight variation of color. This could confuse the next program at the moment where it chooses the color palette for the Animated Gif.
II. Animated GIF does not support alpha transparency. You can choose 1 color of the color palette, to be transparent. You could use the color on the top-left pixel.
III. The fastest is relative. A small animated GIF with no dither, with only some frames, is a good idea. But some other animations will be better served as Mp4 video or CSS animation. Take a look at some options Creating high quality animated backgrounds from Illustrator files