Hi rtorrez!
I had a similar puzzling accumulation of water that I thought for a long time was due to a leak. It came and went just like yours, irregular. On a very light coloured tile, it was hard to see the full extent of water, but it was noticeable on the floor near the base of the seat/bowl. I naturally assumed it came from the wax ring area.
I forget how I went about discovering its source, possibly laying out a bed of toilet paper strips. Turned out to be condensation on the back of the tank near the wall. But only during damp weather! In your part 1 you say the room didn't seem damp, but showers may make the room damp enough to not only cause condensation, but also to cause dripping. That, in combination with wet weather, or wet weather alone, can cause dripping: the humidity inside your house rises significantly during wet weather, enough to cause condensation on the tank. Note that water that comes into your house from underground pipes, is very cold. When this cold water fills the toilet tank in warm damp conditions, condensation is very likely. I suspect the restricted space behind the tank didn't allow evaporation to occur as easily as on the rest of the tank.
In our case the drips fell in the darker floor area near the wall and, due to a slight slope in the floor, made its way towards the seat/bowl where we could then discover it.
We now have an insulated American Standard 6 liter/1.6 gallon toilet; not because of the leak, but in order to save by using less water for each flush.
There are trays on the market that fit under the tank to catch condensation drips. Or you could try hanging a towel behind the tank, provided it's in contact with the tank. Clamp the top edge of the towel under the tank cover to hold it in place.
Good Luck!
Speedy7th.