[MagicRat]

If your cooling system was neglected in the past, there is probably lots of accumulated rust and scale breaking loose and contaminating the coolant. A reverse flush with a good flushing compound would help.
As for the battery and the temp, don't trust those cute little factory gauges. They are not too accurate. Get a good digital multi meter. The battery, with the engine off should have about 12 volts. With the engine running, it should read about 13.7 to 14.5 volts at idle, with no accessories or electrical stuff on.
Sometimes headlights etc can draw more power from the alternator than it can provide at idle. This is normal. But if you must rev the engine to get more than 12 volts with no electrical stuff switched on, your alternator may be faulty.