1. I would change the thermostat, as the leak at your housing is most likely due to the t-stat gasket having gone bad. For an entire $10, you may as well change the whole t-stat out (which should come with a gasket anyway) so you can rule out the possibility of a bad t-stat at the same time. Your high idling temps may very much be due to that leak (allowing air into the system). Make sure you completely bleed the system of air after you're done replacing the t-stat, too.
2. If the whole arm is wobbling on the tensioner, then yes, I would replace the whole thing. It's not very expensive, and it's pretty common for them to go bad as they get up there with age.
3. The stalling and poor gas mileage issues can be caused by any number of things, which can be divided into 2 categories; electrical, or fuel related. The car is either not burning the fuel efficiently due to something not firing correctly in the electrical system, or it's dumping too much fuel due to a something not operating correctly in the fueling system.
a. I'd first start out by getting all three ignition coils and ignition control module tested for free at any number of parts stores. Then, change your spark plugs and plug wires (it's cheap enough to do that I wouldn't even bother with checking them, or be concerned with how recently they were done). The computer is another possibility here, but I'd leave that for last, as it's not common.
b. If you have access to a multi-meter, check the resistance on the fuel injectors, and make sure they're within spec. Using a fuel pressure gauge, I'd also check what kind of pressure you're getting at the fuel rail. Leaking fuel pressure regulators are also very common on these motors with age. I'd also change out the fuel filter since it's only around $12, and should be done once a year or so, anyway.
Everything mentioned above is very common for failing on the 3.1s. I'd start there, and see what you find first.
One thing is for sure you need to get the coolant system fix before worrying about anything else. I’d hose the engine compartment down to clean it out, hose it down after the engine hasn’t run for an hour and stay clear of electrical stuff. Then run it in place and see if you can tell where the coolant is coming from. 
