Truck woes

So my 2003 Explorer Sport Trac is getting a little long in the tooth, and yesterday was a stressful day. Truck sat in the baking sun all day, and then I had to go get little Mr, and when I got him in and going, the heat appears to have soaked the battery because it wouldn't crank with the AC on. Then I was stuck in traffic and it started to rev much harder than usual: idle is about 500rpm, and it was heading north to 1000rpm. When I got to the off-ramp near my house, the oil pressure gauge started to flutter. That's usual given the heat and the fact that the overheated oil is having a tough time