Plexiglass is a brand of acrylic, yes
When you say polished, what do you mean? You don't really want the bonding surfaces polished in the literal sense, you want the prepared as in rough-cut then routed flat/straight or scraped with a razor blade. you should be able to stand one piece on another, or at least close to it. The solvent will bond them together quickly and you won't have to worry about it moving after a few minutes - using something that won't bond to the acrylic to hold it in place will work, like a small block of wood on either side or a brick even.
If you're making a small 5-sided box (open top) then there is more than one way to do it, but the "textbook" way is to build the 4 sides first, lay the "front" panel down, bond the 2 sides to it, then after it dries, flip it and bond to the "back", then bond those down to the bottom. The smaller the build, then more difficult it can get though because of small imperfections being magnified. When bonding the box together, you will want to line up what will become the bottom joint so that you don't have to scrape or sand much, if at all.