In a nutshell, yes.
Second to fourth messages should all have you look at your current position, flight planning & ETOPS requirements. ETOPS determines the maximum allowable amount of time you get between yourself & the nearest available & suitable airport. This is guided by particualr company certification & standards so this can vary between airlines.
Looking at my company, with the APU unservicable or otherwise unavailabe we would be limited to ETOPS 180. If i were to apply that here i would have to ask myself if there are areas coming up where in case of 1 engine failure my nearest alternate airport would be outside of the 180 minutes now still allowed. If that's the case i could not legally continue the flight and would have to divert or return.
Something similar happens with FIRE LOOP1 ENG L where i would also be limited to 180 minutes. If FIRE LOOP2 ENG L were to come on that would be reason for an immediate diverison.
While people usually think of ETOPS in case of an engine failure degraded fire surpression systems can also place limits on your flight. I'd have to look up what would be associated with the BOTTLE CARGO messages but it would certainly be something to look at.