Hello. Recently obtained vehicle from friend and been having multiple issues which may or may not be related. First issues with starting a vehicle. the vehicle had a bad battery when I bought it and basically needed a jump-start every time to start it after a few days of this, it simply would not start and would just hear the solenoid click once when the key was turned. Replaced battery.and same problem. So my buddy did something to run jumpers to the starter so I have to turn the key and push this button attached to the jumpers and vehicle starts no problem. So I guess my question in this instance it is what the problem because I have a good battery in there now so is it my connections to the battery itself or?
the other issue that I feel arose as part of this problem it is the heater stopped blowing on high basically after he did the bypass to start the vehicle. It also wont blow hot for a while before it gets warm but then all the sudden the vehicle to overheated at idle which makes me wonder if the heater not blowing on high could somehow related to the radiator fan or something? It doesn't overheat at speed and it'* like 0 degrees out where I'm at right now It'* an old car it'* got a little miles I realized a lot of stuff can break but I'm just wondering if these issues are all related potentially

I would start by looking through the entire electrical system. Check all cables for corrosion. I would also check to make sure that there is not a substantial draw that is draining the battery dead. Also check the fuses and wiring and see if you can track down why it is overheating. If I had to guess, there is an issue somewhere in the power distribution side.

Some of the things you mention have relays that run through the main power distribution block. The High speed of the HVAC blower usually is on its own relay. Cooling fans are run by relay, etc.

At one point on my Regal, I had a loose wire going to a power distribution block, and the only way I knew about it was that the starter wouldn't engage, and there would be times the vehicle would quit running, with a wonky voltage reading. They would jump start it (applying power to the loose connection) and then it started right up. Once I found and tightened the connection down, no more problems. It happened to be the power block that had the starter relay, and some switched circuits on it.

Check and clean the battery ground cable where it attaches to the engine block.