APU HOT BAT OVHT light – can’t say I’ve ever seen one fitted but I’d guess it either means – don’t try an APU start since the battery is hot and could be damaged. Or more likely, the battery has overheated and charging has been stopped to prevent thermal runaway. On the Elec panel would seem a good place to put it.
Buffet Alert means that your sandwiches are on the way.
No? Sorry. Ok, my notes define the message as “at current conditions, the airplane has a buffet margin less than that selected on Perf Factors page”. The buffet limit envelope is stored in the FMC performance database.
All the ANS systems I’ve seen use IRS unless anyone knows anything more.
Your operator must have picked all the options possible when they brought these.