Radio Shack carries the replacement batteries for ALL of the Macs you acquired. Be prepared for sticker shock as far as price goes on those batteries; they aren't cheap, especially if you have to buy lots of them. Though, you might get a discount for buying multiples of the same product.
If you need a proper screwdriver to get into those Pluses, here's a simple solution: Stop by your hardware store and ask for a T15 with a long shaft. Or get one of those extensions for socket tool sets and get a T15 bit to match the extension. Most extensions will have a magnetic tip, so be careful around floppies and hard drives. You can also take a T15 bit and stuff the end of it in a Bic pen and use that as an extension. There are lots of possibilities.
The "flashing in and out of contrast" could be a dusty brightness control potentiometer. If there is a knob in front of the computer below the front of the screen on the left side, that is where the problem exists. You could carefully open up the case, and either spray some contact cleaner somewhere in the pot or you can replace it with a new one of matching value. This would mean desoldering the old and resoldering in the new. If you don't feel up to soldering, get the help of a friend who is good with soldering.
73s 8)