Ligatures or Two Letter Equivilents

I'm curious who uses them.

Examples: fetus or foetus; encyclopedia or encylopaedia; demon or daemon.

Do people in the UK use the ae/oe spellings of these and other words, or are they falling out of use.

In NZ we tend to still use the ae/oe spellings but I never heard demon spelt daemon.

We still kind of have them in US spelling, altho they're much less common. There's variation in a few words like "aesthetic/esthetic" and "archaeology/archeology." I see all those forms pretty regularly, and personally prefer variants "esthetic" and "archeology" because they're slightly simpler and I think they look nice. "Subpoena/subpena" is an example where the "oe" is almost universally preferred in popular texts, as "subpena" hasn't really caught on (many American dictionaries don't even list it), altho official government code and sources use and endorse the "subpena" spelling. In the domain of science, in particular, American usage has steadily drifted toward dropping ligatures--older publications and textbooks I've seen usually preferred "amoeba," while when I took biology in high school a few years ago, all our texts and materials used "ameba" exclusively.

The usage of demon/daemon is also purely an aesthetic/esthetic choice. Though the only non usage of demon/daemon is in internet terminology with a mailer-daemon (automated email processor who tells you why your email wasn't sent). I've seen in computer games the usage of daemon but that really is not important.

In OZ like NZ, we tend to use ae/oe - I've seen daemon

And then there is manoeuvre, I think I've seen that spelt differently too

"Manoeuvre/maneuver" is an interesting case, because it's a bit different than the others. The "oeu" in this case was directly taken from French, and French "oeu" is historically different than the "oe/ae" taken from Classical Latin and Greek words (which is also why a great deal of technical/scientific/medical words in English are the ones with these ligatures). However, languages like French and Spanish have long since eliminated the Classical Latin and Greek ligatures. Compare French "archéologie" (arch(a)eology) and "diarrhée" (diarrh(o)ea) to French "manoeuvre." However, no matter the etymology, American English still exclusively prefers "maneuver."