The alt/battery is not related. However that likely means you've lost the regulator, fairly common for that generation. It could be the alternator itself, but I'd shoot for a regulator first, unless you also have bearing noise.

On the misfire, I'd vote on an injector as well. If you don't want to dump more money, swap it with 5 and see if the misfire follows it. If not, then it may be the injector connector, there are repair kits readily available for that so apparently they're not 100%. That said, I'd think a failing connector would cause fuel starvation in a cylinder, not overfueling. Still, I'd swap the injector with the next cylinder and see what you get.