Post-12V battery replacement instructions?

My wife was driving our '06 Prius when a plethora of warning lights came on in the dashboard:

1. red exclamation in a triangle,
2. amber malfunction indicator lamp,
3. amber brake system warning light;

On the central console screen:

1. hybrid system warning light (car silhouette with red exclamation point).

I did a quick search online to find most forums suggest either water pump recall or 12 V battery replacement. Our water pump was replace already, so I began to explore the 12 V battery. I did the "Display button + 3 light flashes" to get into a diagnostic menu. Battery was at 10.1 V so I replaced the 12 V battery DIY. Voltage reading is now 12.8 V, so I thought I was good to go.

After the battery replacement, all the original indicators remain on. Does this indicate additional problems or do I need to somehow reset the system?

Some additional peculiarities (even after battery replacement):

1. battery fan beside right, rear passenger comes on pretty much as soon as car is started (when I replaced battery, I did a check to find the ducts were indeed clear). Fan is loud! It's a balmy 80 degrees.
2. battery charging indicator on central console display fluctuates greatly (I thought this would have changed since replacing battery)
3. when I punch the gas pedal and immediately release, the engine revs for a unusually long period of time (relatively speaking, 3-4 seconds)
4. when I punch the gas pedal and hold it (ie accelerating onto highway), the engine will sometimes rev up and drop 2-3X even though I am not changing pressure on gas pedal

Thoughts? Advice? I was hoping the battery replacement would cure all, but I am now skeptical.