These sound like simple electrical connections / contact issues. Look at the top front of the transmission and you will see a plug with two wires connected to it. This is the tach sensor. Pull these wires, they are simple press on fittings that press onto a spade. Spray them with WD40 or Boshields corrosion block spray and then press them back on. Make sure they are tight, if not crimp them tight. This should fix your RPMs. As of the battery light, I am not sure what or where that is, but it has to be the same issue. Simply check the connections, clean, and re-tighten. Loose wires casue all kinds of problems and we look at as tighten all we can every year.
Hayden