What are the basics of making a rechargeable battery pack?
You can't just connect an AC adapter to a bunch of rechargeable batteries directly.  Instead you need to have some sort of supervisory circuit to shut off (or taper) the charge when the batteries are fully charged.  These days that is usually done with a specialized IC doing most of the work.

Here is a charging circuit that supposedly works with up to 8 AA NiCad cells.