Only things i can think of are the Oil pump gasket, or the valve cover gasket near the Cam seals or also your oil filter housing, those seem to always leak.
You can also check the bolt that you use to tighten the alternator to the little bracket and make sure its not stripped that might be the reason it keeps on comming loose, i now cause this happened to.
Ok here's a quick an easy way to find out your alternato is bad. Turn on your car go into the engine bay and disconect the positive side or your battery. If your car shuts off then you have a bad alternator. Or you have you checked the Fuses by the battery it might be blown.
I do as well i been taking apart 1g's since i was 16 with my cousin's. Its like Bud92gsx says with the right research you can take ont this project. And the first place to start is by buying a Haynes manual for your 99 eclipse and of coure here on DSM TUNERS. Good luck!!!