How to interpret these codes and symptoms?

I hope, someone came across the same issues and can help me figure what needs to be done with my car.

I have a rather worn 2012 Prius C with about 160K on it. A few months ago, I got a check engine light, which was due to P0A80 code, and it was the only code detected at that time.

I kept driving that car normally, as it was fully functional, and I was thinking about buying a different vehicle, so I was not sure if it was worth replacing the hybrid battery or battery cells. Recently, the battery capacity started declining, it seems, because each time after resetting the code, it was soon appearing on the dashboard again.

I searched and found a decently priced used battery from a much newer Prius C, and I decided to keep this vehicle and replace the battery, now just waiting for it to arrive by slow freight shipping.

A few days ago another problem started. As I was driving, I got a [Break system warning light] and [Slip indicator light]. At the same time the hybrid battery fan at the back started working loud and non-stop. The car was feeling sluggish at higher speed, which never happened before. Autozone code reader confirmed the existing P0A80 code, and added front right sensor issue. There were some details about possible circuit issue at FR or metal object stuck to the sensor. I tried cleaning the sensor, then replaced it with an inexpensive generic one. That did not help at all, and those lights appeared again. Also, now the car does not always start with the first full turn of the key, it only lits the dashboard. But it starts the second time you try.

My question is: could all of these be the result of a failed hybrid battery, or is there definitely a real problem with the sensors or breaking system? As I understand, regenerative breaking stops working normally with the hybrid battery failure, and it may slow down the vehicle. Also, hybrid fan behavior is a sign of a failed battery. Because both of these happened at the same moment, I suspect they were caused by the same underlying issue. Does it make sense to just wait for the new battery to arrive, or should I keep searching for another problem, which is causing the new codes?

 

I forgot to mention. When all those indicators are on the dashboard, and I turn off the ignition, there is a lot of shaking in the engine area for a second. And if those lights happen to be off at the moment, there is no shaking.