Bad electrical contacts is a very common cause of a multitude of problems in Z cars. They cause many people to start buying expensive new components they don't need. (I'm one of them.) My suggestion to you is to go through EVERY electrical connection under the hood — disconnect bullet connectors, fuel injection plugs, battery terminals, all body ground wires, etc. — one at a time. Then clean both ends of the connector as well as you can with emory paper, steel wool wrapped around a tiny drill (good for fuse holders and bullet connectors), compressed air, whatever. Recrimp or solder any that seem loose or sloppy. Then reconnect. I can almost guarantee the car will run at least 25% better after just doing that — and in a car that's sat for a long time as it sounds like yours might have, I can also almost guarantee that you'll find powdery white corrosion on at least one or two connectors in the process of doing this job.
Of course, the problem could also be related to the installation of the alarm. But try the connector cleaning thing first and see if it doesn't solve the problem. Frying wires (or fuses that melt the fuse box) are a very common result of dirty connections.