Lighting, Light Fixtures, Ceiling and Exhaust Fans - Multi Switch Ceiling Fan Puzzle

Here is the present situation with reinstalling a ceiling fan.

Moved into relatively new home (10 yrs old). Installed new ceiling fan in mstr bedroom where one previously existed.
Mounted and wired fan properly, to existing junction box.

Fan works with remote keypad as follows: On button and H/M/L speeds on remote work once right side wall switch is turned on. Fan shuts off when same wall switch is turned off or "off" button on keypad. Remote "on" button will NOT turn on fan if wall switch is off. It appears the wall switch has control of incoming power.

To further confuse the issue, this wall plate has 2 single wall switches behind it. I have a lamp plugged into a wall recepticle just below this wall switch that is not controlled by the other switch. It must be turned on manually.

Also, the opposing wall across the room next to the closet door has the same dual wall plate with 2 single switches. One switch does in fact turn on the closet ceiling light. The other powers nothing that I can see. I have plugged in the lamp to all receptacles to test the other switches with no luck.

So, both sides of the room have a switch that provides power to something visible and a switch that does not activate anything at this time.

I am guessing that at one time they might have cancelled each other out, like a 3-way switch to inline lights? Or the previous fan also included a light.

What would be the best approach (steps) for testing this circuit (s)?

DMM, tracer, etc.
Please advise....

Are either of the unknown switches marked with ON/OFF or are they blank?

Did you check both the top and bottom half of each receptacle for switched operation?

When you wired the fan how many and what color wires were in the ceiling box?

Are either of the unknown switches marked with ON/OFF or are they blank? Will verify this evening

Did you check both the top and bottom half of each receptacle for switched operation? Will verify this evening

When you wired the fan how many and what color wires were in the ceiling box? I installed it sometime back and will have to remove for accuracy

PCBOSS,
Yes, the sister switches on both walls do in fact have no on/off lettering embossed on the toggle.

Also, I pulled the switches and rediscovered that these 2 with blank toggles are wired this way:

One has 1 black wire and 2 reds, the other on the opposing wall has 2 black wires and 1 red.

I am assuming that these are travellers that controlled a light for the previous fan that was installed??

I'm not sure you have any problems. It seems to me that everything is working as you would expect. If you want to use the remote control for your fan, then leave the wall switch on at all times. Turn it off when you go on vacation or other times when you won't be using the fan for extended periods.

If I leave it alone, I agree.

Since I do not have a light installed, I am considering rewiring
those switches to the outlets below them. Thanks both for your input!

Since I do not have a light installed, I am considering rewiring
those switches to the outlets below them.May or may not be possible. Just in case, leave yourself the ability to return it to how it is now.