Square pixels: Are you sure you’re not just drawing with a large brush in Piskel? It’s only the 1x1 size that draws individual pixels (in both Aseprite and Piskel), anything larger will be some shape made up of many pixels, and this arrangement can have a variety of shapes depending on the brush. If you want those larger shapes to be squares, you’ll need to use a square-shaped brush. Aseprite definitely supports that, and Piskel probably does too. If you just want your pixel art bigger, then draw it small and export it larger.
I can’t answer question number two for certain, but probably not, you should be able to keep your compiled Aseprite, as long as you keep it somewhere different from the installed one. Aseprite is pretty portable, so you shouldn’t have any conflicts.
I think Discord always pops up a warning for links to domains you haven’t visited from Discord before.