Jim Beaver wrote:
1. Two of the alarms (of the same type/brand) beep three times in
succession, a couple of times a day. But I can't get them off the
ceiling! I've tried everything I've ever known or could learn about
smoke alarms to get them to unlatch, so I could change the batteries,
but to no avail. There is no marking anywhere I can find on the
outside of the alarm to give me either instruction for opening or
even the brand name. I've twisted, turned, pried, and prodded them
and cannot get them loose from the ceiling without pulling down the
drywall.

Three suggestions:

1. Push, then twist.

2. What's it look like on the other side of the drywall ceiling?

3. Perhaps the alarms are reflecting the condition of the CENTRAL battery?
You said they were hard-wired, maybe there's a large, universal, battery
somewhere.