Need some help miata wadesboro nc/pageland sc

I was on my way to pageland to stay the night before a track day at cmp for the next two days. I got stuck in a crazy downpour pretty much could not see. I pulled off in wadesboro and grabbed my paper towels as the defrost wasn't working to clear the window. Got back in the road and noticed that the charge light was in and then I saw the temp gauge was pegged. I immediately looked for a safe spot to pull over but then I heard a psssh and the gauge was reading normal temp. As soon as I found a spot to stop safely I pulled off anyway and shut the car off. My alternator belt is completely gone and I think it drives the water pump as well which is likely why the charge light was on. I did not see any vapor or notice the car running oddly before I turned it off. There is still coolant in the expansion tank however I did see some coolant on top of the radiator. 

How do I determine if I have more serious issues than the missing belt? 

Because this belt drives the water pump did I likely hurt the engine? 

Best way to tell is to replace the belt and fire it up. Miata head gaskets are pretty strong.

Now, do you know the age of the belt? Maybe it just died due to age. Or maybe you've got a pulley walking around due to a loose bolt. The former is more likely, but you'll know the car's history.

The belt was brand new I had replaced it when I got the car. I do remember the alternator adjustment bolt feeling a little clunky. Should I try to replace that or the alternator also? It was pretty squealy on a cold start for a few

What am I looking for when I do fire it up? 

In reply to Jaynen :

If it runs fine, there’s no coolant in the oil, no oil in the coolant, no coolant out the exhaust, and no leaks, then nothing got hurt. 

If the belt was squealing, it was slipping. I’d chase the threads in the adjustment block for the alternator, throw a spare belt in the trunk and try again. The alternator light will give you an immediate indication of  another broken one. 

The belt was gone entirely, and with it being the alternator one it must have snapped. My guess is getting doused with standing water caused the belt to slip, overheat and snap.

The psssh I heard has now been proven to be the top of the radiator popping (plastic but a newer non original one)

Still not sure about headgasket yet until I replace the radiator.

Is it safe to use the engine to get it off the trailer/park it not like driving around or anything? I pulled it onto the trailer using the engine the temp gauge was normal but this is after the radiator blew and I shut it off immediately after

If you're starting from a cold engine, you can run it for under a minute without doing anything terrible. Just don't spend a lot of time idling - fire it up, get off the trailer and shut down. 

Bummer about the rad, but at least you have a known problem to solve!

Well, I was thinking with doing track days "in da south" I might need to upgrade it anyway. Wonder if I should do the coolant reroute also?