About 4 months ago, I came home to a partially flooded basement close
to where our furnace stands. When I investigated, I found that the
drain in the floor nearest to where the furnace condensation pipe leads
in was completely backed up. After sticking a wire down in there, it
finally released most of the backup. My question: is water supposed
to remain in this floor drain or should all the water be drained out?
I still have a little bit of water sitting in there at all times and
didn't know if this was normal. If water is not supposed to be in this
drain, how do I clean it out?

Can I also use this same drain for draining my hot water heater as
well? Thanks in advance.

You're probably looking at an in-floor connection to the local
water-table, rather than what you seem to perceive as a piped drain.
Often it's just tile pipe to nowhere.

I've seen strange things happen with water level in such
"hole-in-the-floor." Like, after decades of a dry-hole, suddenly water
poured forth. Seems something changed subsurface water situation in the
area of the house. Then it flooded another half-dozen times.

Simplest solution: float-valved sump-pump.
Severe case: work on drainage around house perimeter.

J

If it is a sewer connection it should have an s-bend or some sort to
keep a water lock to prevent sewer gas from entering the basement.

The ones I have seen have a removable grate cover to prevent debris
from entering.

If it an old pot style drain it may be less than 12" deep but will have
a pipe entering the side near the bottom.

You can use it for draining anything in the area but code may require
an air gap.