[Vespasian]

Do emergency services work on Shabbat?

If their apartment catches on fire would a very orthodox person be allowed to use an extinguisher / carry out some of their belongings?

[dvirsky]

Sure, there is a principle called Pikuach Nefesh (https://en.wikipedia.org/wiki/Pikuach_nefesh) (literal translation - watching over the soul) which means that anything that endangers people's lives is more important than Shabbat. You can certainly drive to a hospital or call 911 or whatever if it's a matter of life or death or an emergency.

[jaza]

Not just Shabbat:

"Pikuach nefesh ... is the principle in Jewish law that the preservation of human life overrides virtually any other religious rule."