Hello musto,
The battery went through more than 500 cycle, that is a lot. Please refer to below article.
ASUS Battery Information Center
If you think that the battery life issue troubles you, then you may change one.
When the AC is plug in, the performance of the laptop increase and the heat would goes up, so of course the fan would spin faster and become louder.
It became louder than before could be that there is dust in the fan or the heat radiation of the laptop is also decreased.
Maybe it's time to back up your data and reset? to have a fresh start? the freezing issue could be related.
Thank you.