All of your symptoms sound like a faulty Neutral connection. Faulty neutral causes L1 to affect L2, and has no affect on 220 equipment just like you described.
Fix that quick. A faulty neutral can damage your equipment, and because you installed a second ground, it can harm YOU as well. Check that the neutral wire is firmly connected, and using Noalox:
ALL aluminum connections for that matter should be protected from corrosion and thermal expansion with Noalox.
You are lucky that you have a conduit! You have an EASY way to remove the entire length of the neutral conductor to inspect it for damage. You should also take advantage of that conduit to pull a ground conductor through it and use that to ground your sub panel VIA your main panel. Do not use a second ground rod at the sub. It is not worth the risk in your case.
No, do not replace everything.
Do you have a proximity based AC detector?
Do you have a signal-toner? (wire finder)?
What has changed (if anything) recently with respect to light fixtures, wall outlets, switches, extension cords, etc? Especially and obviously on this circuit specifically? Did you add/remove anything new? (a heater, an AC...)
The flickering for the bathroom light fixture that no longer works was probably your indication of a problem where somewhere a splice is detached (wirenut, backstab, wall sagged and tore some romex)
Has there been any new work activity in an attic or a basement?
Anyways....
As/If necessary, isolate all power and either use a toner or a detector with the goal of identifying all points of wire junction on the circuit in question. Positively identify anywhere there could be a BOX (switch, outlet, light etc.).
Using the above, make a logical path from the circuit panel to each room. Where would you run the wire FIRST if you were an electrician and didn't want to waste money on wire? Focus more on any common points near the affected area. NOTE: common sense doesn't always apply with how they run the wire, but it's a good guide.
Mark off any items that had "a lot plugged in" or that people bump/wiggle a lot.
Secure power to the circuit in question if not already.
With your list of suspects, (key suspects are ones that were not working) take a wall plate, or light fixture off and pull the wiring out. Ensure all wirenuts are secure, nothing is loose, burned, or dangerous looking. If so, repair it.
Pay close attention to any non-ground wires under a wire nut (more than 2) or in a backstab (more than one, or better yet, NONE!) or double upped on a screw.
If backstabs are used, take the time to correct this.
If wires are more than one to a screw, correct this.
If there are more than 2 wires on a wire nut, inspect it. One of these wires may be the suspect causing the outage.
Do not resume use of the circuit until you identify the bad connection. It is a fire hazard.
Depending on what you find from the guidance above, you might want to do the whole home. The issue you are having "should never happen"
Lastly, and this could have been first - do you have aluminum wiring? If so, there is a completely augmented list to follow.
Best Answer
To me this sounds like a bad connection, if both rooms share a common wall and the receptacles are on that same wall it is very likely you have a loose connection on the neutral white or hot black , most common is a backstab failure the push in connectors. Usually the last working receptacle or first non working one is normally the location of the failure, you need to figure out where the feed comes from and find where the problem starts, work from the location that is closest to the breaker panel. The last working device or first non working is normally the point of failure.