Removing the discoloration in terrazzo from moisture or glue is a toss up. You can do several things to lighten it, but I wouldn't guarantee total removal. Depending on the texture of the terrazzo, you may have to start with a 70 grit metal or copper bond diamond to get it all smoothed out. A lot of times terrazzo takes on a snakeskin, or lumpy texture from years of abuse. If this was the case and just covered with carpet, then you need to grind.
As far as patching goes, it's kind of the opposite of stone. You want to open up cracks to get (matched) aggregate in there with the epoxy so it blends well when you finish.