How can I determine which equipment in my basement is beeping periodically?
It's almost certainly your FiOS ONT. The power supply contains a battery, and it beeps when the battery dies. You can take the battery to a hardware store and buy a replacement for a couple of dollars, or call FiOS and they will send you a battery.

Those other deices you listed usually don't beep, except for the sump pump if it's got a water level alarm or a battery backup, but usually the water level alarm is constant. It may have indicator lights to tell you what's wrong.