Car keeps overheating?

So long story short. I just bought the car listed above about 5 days ago. The guy I purchased it from told me that he bought it 14 years ago and after he bought it he ended up getting locked up for 14 straight years. So he just got out and the car had been parked in the family's garage the whole time until that very moment he had drove it to a mutual friends house to sell it to me. That was the first and only time it had been driven before it was sold to me. He told me that he thought it was a rear main seal that needed to be replaced but after driving it for the first time I don't think that's the problem now it has been overheating for me since I've bought it getting all the way up to 250 and 260 coolant level that's pretty hot anyways. I've been putting water in the coolant before I drive and I noticed a slow leak under the car which what was weird about it is the faster I drive the more cool down the engine would be and sometimes I wouldn't even need to top it off because there would still be water and coolant in there, but then other times it'd be completely gone in the matter of minutes. So I replaced the thermostat because the old one was stuck. When I replaced the thermostat I noticed that the radiator hose was not squishy it was hard so I kind of inspected more of the car the radiator fans wasn't working. So I splice wires and connected it directly to the battery and the radiator fans came on. So they were working, but after I replace the thermostat the fans came on by themselves. So after replacing the thermostat and and reconnecting the hoses after I patched up a little bit of the small leaks that were coming out of the hoses my car still overheating, for some reason and I can't figure out why, there's no more leaking on the ground under the car. What do you think it could be?