2007 error codes: help with diagnostic repairs?

Hi there,

Second-time Prius owner. First in the US, now in the UK.

I have a 2007 Prius which has 330k miles, and I realize it's time to do some maintenance. Just bought over two months ago.

I suspect there is an issue with the Prius hybrid battery; I took it for a spin after five days away, and it went into 'limp mode' with the red triangle of doom appearing on the way, so I turned around. Here are the codes, which I obtained through Car Scanner using a Veepeak OBD2:

C1628, C1641. Are these related to the ECU or spark plugs?
P3000, P0A80. This is the major one. Suspecting the hybrid battery will need replaced? Or, is it possible this is a product of a cold snap? I tried to run a Dr Prius hybrid battery health check, but the test stops halfway through, stating that the hybrid battery is too cold to proceed with the test.
P0420. Knew about this at the start; the cat will need replacing soon. However, it passed emissions on the MOT (done earlier this month).

Any advice would be greatly appreciated!