Toyota runs fine but has trouble starting sometimes

I know for sure my starter relay works, and my starter itself. My 80amp alternator fuse was blown until my dad saudered it. When it doesnt work it clicks, then after you let it sit for a few minutes it starts or it makes a sound that sounds like air or the fan wants to turn over but doesn't have enough power. So me and my dad checked my battery, it said 12v, then we got it to start and it was running 14v. The things that are broken or not running properly are the clutch slips/clutch fan, both 0'2 sensors, front fuel filter was replaced with a used one. Has another weird problem when it rains, seems like it loses power and backfires and feels like you are popping the clutch when you have the gas to the floor inorder to keep it running. I plan to get everything fixed but want to get the engine and everything else running smooth before fixing the easy stuff.