Drum Brake dragging? Constantly charging battery.

That was just the car doing what it's supposed to do. You were picking up energy downhill, and the battery couldn't hold any more, so the transmission sent that energy off into spinning the engine faster to hold your speed down. If you had been in a manual-transmission car, you could have downshifted then for a similar effect, and the engine would sound the same.

That's P0A80 (there's never a letter O in a trouble code) and it's just telling you your next round of battery module whack-a-mole has arrived (or it's time to abandon whack-a-mole and buy a battery).

Again, as described first above, that's just the car downshifting for you to hold your speed down, once no more energy can go in the battery. That's normal behavior, but it can happen more often or on shorter descents if your battery is old and tired, because there's less battery capacity to fill before it happens.

Yes, this is another issue, so you've got more than one thing going on. It would be best to post the trouble codes when that happens. If you don't have a scan tool that will show you all the trouble codes in the car (many won't), you can get the codes from the brake system without any scan tool at all, this way:

Blink (a/k/a Flash) Codes – How to. | PriusChat

 

If the OP often goes down a long hill so that the pack fills up it might be worth considering turning on the headlights, defrosters, AC, radio, and anything else that uses power. (Run the power windows up and down?) That will reduce the energy going into the pack which will in turn reduce the risk of the pack overcharging. There is also "B" mode in the transmission, except while I am sure that will increase braking I am not sure that it would not make the overcharging problem worse.

 

Shifting to "B" is the go-to method for reducing charging, using engine braking instead. Toyota doesn't document this very well though.

 

^ this.

While B mode does give you an increased braking effect, it also changes the car's bias to be a bit less aggressive charging the battery, and a bit quicker to use the engine to spin the energy off. It doesn't make anything happen that doesn't also happen normally in D, but it changes that balance.

It is the normal, recommended way to drive down a long descent in order to be nice to the battery.