I prefer using Easy Gif Animator Trial Edition.
And how to easily animate is to make a Big enough PNG filesize, usually around 64x64, with transparency background, and then have your sheet beside that in your own Paint Program(I prefer PSP), and then copy and paste each and every sprite of the sheet one by one, then after each time I pasted it correctly, save the file in the 64x64, then alt tab to EGA, insert image, and then use the newly resaved PNG file, then alt tab back and paste next sprite and repeat that.
makes animating sprite sheet alot quicker and easier to make it look correct.
Part 2.
I got to say I'm impressed how fluently you made these animation in such a small resolution.