Ford Probe is doing some really strange stuff

1996 Ford Probe 4 cyl. 2.0L, 126700 miles.

The best way to describe the problem(s) is probably just to tell the story of what happened. Driving back from Orlando International Airport to Gainesville, FL, (about a 2 hour drive) about 5 miles into the journey I noticed that my engine temp. Was much higher than normal. I immediately pulled off to the side and checked my coolant levels, which were fine. Got back in the car and kept driving, keeping a close eye on the temp gauge. After it started heating up again, I pulled off the next exit and to a gas station, where for good measure, topped the engine coolant off with a little water. Got back on the highway and drove for a while, and now i'm noticing what would be an obvious correlation, that when my tach. Is reading about 2500 rpms, the engines heat starts to spike, but when I maintain lower than this level, the temp. Is about normal. At this point I also noticed that my battery gauge was extremely low. Nonetheless, having to maintain a constant, fairly low rpm, my speed was somewhere in the 40's or 50's, and my trip would be long. When the bat finally went, I lost my gauges with the exception of the gas, oil pressure, and engine temp, so I decided at the next service station off the highway, I would stop to see if a mechanic could at least tell me what was wrong. A AAA mechanic checked my belts, fluids, and cooling fan, telling me it could be a water pump problem or a thermostat problem. He then put a meter on my bat, which was dead at this point, and told me that my alternator was now shot. Nonetheless, I had to get home cause of classes the next day, so he hooked a jump box to the bat, I started my car and I drove off. I got about 15 miles from home at that same slow pace with no gauges or battery power whatsoever. Now since the bat. And alt. Were done, if I let the car idle, it would stall, making slowing/stopping the car(automatic trans.) Interesting. I had to shift the thing into neutral, keeping my foot on the gas giving it a sufficient amount of rpms, using my left foot for brakes. When I had to speed up shift back into gear with the accelerator still depressed. This worked for slowing down, but when I went to stop, I tried the same idea, but the car stalled and ended up dying. Had it towed back to my house, and it's now in the driveway. Is this strictly an alternator problem, or did the AAA guy forget to mention other problems?