My half bath has a small ceiling fan and light bar on one toggle switch. Can I wire them seperately into a single gang with 2 toggles? Thanks folks!

Symptoms: 1. All countertop outlets in (3) bathrooms - not working. 2. All (4) outside house outlets - not working. 3. All (3) garage outlets - working. Yes, working. 4. House built ~ 1980. History: Everything (the outlets) working normally. Then two things happen simultaneously (so, I can't pin it down which might have caused the problem). I put up outdoor Christmas lights, and I had a work crew working on my swimming pool (tiling, coping, decking, etc). The lights work fine the first night - then they wont come on the 2nd night. Outlet is dead. Pool crew works another day - their last). Then the lights work again. "Maybe they reset the breaker," I think to myself. A week goes by, outlets are working fine. Then I plug in my air compressor (12 gallon, 3 hp, 110v) to one of the outside outlets. It makes about 1 cylinder pump cycle and then nothing. All the outlets are dead. No circuit breakers are thrown. There is one GFCI breaker in the panel. It is NOT thrown. But I press the test button, it flips, and then I reset it. I also flip off, then back on, the breaker for the outside outlets. Doesn't help - still no power. What I tried: I pickup one of those little outlet testers. Test all the bathroom and outside outlets. When NOTHING is plugged into ANY of the outlets, the tester lights up as "normal". If I plug even a small load (7 watt nightlight) into any plug, then the tester (I tried it on all outlets) shows "Hot and GND reversed" I also measured the voltage at the breaker with the nightlight plugged into one of the outdoor outlets, thinking the breaker may have gone bad. No dip in voltage when the light was plugged in. So, I think the breaker is good. I know what you're thinking (because I did, too). Find that darn GFCI and reset it. I have searched hi and low... under sinks, in closets, in the garage, in the breaker panel - no joy. I called the original owner (who was a home builder) asking him where that darn GFCI switch was. His response was that there wasn't one for the bathrooms/outdoor plugs (hmmm...how can that pass inspection?). The tester is the type that also has a button that is supposed to trip GFCI's. When I push it, nothing changes, nothing trips. So, now I'm thinking I have a loose wire or bad connection somewhere. I open up each of the outside and bathroom outlets, pull the wires out of the backstabs and use the screwposts. I also find one nearly broken neutral (white) wire in one of the bathroom outlets. I cut it, strip the ends and re-connect with a wire nut. I think I've beaten this thing! But I am wrong - nothing has changed. There is enough power to light the tester's lights - but any real device plugged in does not work and causes the tester to show the HOT/GND reversed indication. I'm out of ideas. I'd like to hear what others think could be the problem. Thanks in advance, Brian S