With the swelling that ground has, I'd peel it back and make sure it's not growing.
As for the split on the positive, I wouldn't worry about that. Slap some electric tape over it and call it good.
As for testing the regulator, once the truck is running, find an auto parts store that has a battery/alternator tester. You hook it up to a battery, and it tests the system, checks for AC voltage and regulator performance. Just also remember it's a stock alt so amperage won't be that high.
I'd you find someone with a Carbon pile tester, you could test it that way too, apply 70 or 100 Amp load, depending on which alt you have. Should hold the load no problem. Then use a digital multi meter to check for AC ripple. If all is good, then alternator is fine.
I'd check for parasitic draws if the batteries keep going flat.
If you reeaaallly wanted to get crazy about it, clean all your grounds. Mostly the one under the dash next to the fuse panel, where both battery grounds attach to the frame/engine, core support grounds. Also wouldn't be a bad idea to clean all the positive connections too, such as the ring terminals on the starter solenoid and the alternator connection.
Pretty impressive how much of a difference cleaning hot and ground points makes a difference.
And like idibronco said, a good low Amp charger takes days to recharge a battery with minimal damage.