I installed both freeze plugs yesterday which was dead simple. I also plugged the weep hole from the water pump with a whittled stick

The tractor has additional problems I believe.
It took a bit to get it running (low battery voltage from sitting, charger helped, but it still won't turn over most of the time, just sits there). When I can get it to turn over, it runs but won't get full power at all. The water pump bearings were complaining a little bit and it will need replaced for sure. The tractor ran for a bit then kept dying with some black smoke evident. Before it died it kind of sounded like it was starving for fuel. Here are a couple of thoughts I had:
The previous owner changed the filter, but didn't bleed the fuel system. I figured once the tractor was running, the air would purge from the system and that would be it. Does this happen or could there still be air trapped in the lines causing this problem? The tractor has been run about 10 minutes since I've owned it.
Secondly, I started it when I got it because I figured the only problem was air in the line, and I didn't realize that the coolant was gone. Stupid of me I know, but in Texas, the last thing one would think about is a frozen block. Anyway, I let my son drive it and it overheated and died after about 3 or 4 minutes. I didn't realize that was the problem and so I started it back up, saw the temperature gauge, and quickly drove it into the barn as the needle rose and I shut it off. Any chance I damaged the engine so that it would run, but not make full power?
Right now I'm limiting the amount I spend on it until I find out if the engine is operational. I plan on bleeding the fuel lines tonight and seeing if that helps. But if anyone has any thoughts, I'm all ears.