Cooling system

I am working on my daughters first car (2.0L) and the thing has problems. It started with dying (as per her stating or mentioning it to me)so I figured I better look into it.I didnt want her on the side of the road if I could help it. Somehow during me looking into it and my list of questions I was asking her, we stumbled onto the fact it had got hot or at least the gauge went to "H". I replaced the thermostat and repaired her coolant expansion bottle. (It had 2 cracks on the top where the hood rubbed and made contact). I went to start it and had quite a bit of difficulty. It had spark but the plugs looked wet. I replaced the plugs and it acted like it wanted to start. It finally started and ran strong. It took forever sitting there running before the temp gauge would rise mid way. It sat there and didnt move. I thought I had it licked. I test drove it up the street and it gradually rose above mid way twice and then dropped back to mid way. I thought great it is cycling as it should. About 1 mile down the road I started back home and it went to the "H". I pulled it in the driveway and left it running, popped the hood and right then heard the patch job let go. The coolant went beyond the "Max" and almost filled to the top of the bottle. While this was going on the temp dropped back to mid way on the gauge. I read every post on this site and pretty much came up with #1 the system needs to be bled #2 Leaks #3 these cars are notorious for head issues. I pulled the car on an incline and allowed it to run with the cap off and the heater on high. (The heater does not get hot at all) It will sit there and bubble from the one hose all day long if I would let it. The level will stay at MAX with the cap off. No milky oil, no noticable smoke from tail pipe, no oil in collant bottle. I just really would like this to be simple as this is her first car (and she bought it herself) at 18yrs old. The car has difficulty starting when its cold or cooler. When its been ran or its warm, it fires right up with no issue. Runs smooth too. The fan will come on when it gets warm, but when it does, it does not go off until the key is turned off. I think I have covered all the details I can, thank you.