Toto questions

I have a fairly new Toto Drake. Installed about 4 months ago. Love the flush and quick quiet refill, but the toilet's behavior seems quirky.

1. Toilet stopped filling after a flush altogether. Took apart fill valve and found nothing in the filter or anywhere else blocking the water. Tested the water flow with valve apart, plenty of water. Reassembled the valve, toilet filled fine several times. Float does not seem to stick. Anyone know what's up with this?

2. Fill valve sometimes "runs on" for a bit, say 4-5 minutes, after filling. Not a lot, just enough to hear.

3. Wife claims (although I DON'T believe her!) that a few times, after flushing and leaving the room, that the toilet flushed again all by itself!

4. Flush is brief, only about half the tank of water, and refills in 20 seconds. Seems like an adequate flush, but I just want to know if this is "normal" for this toilet. There is a red flapper with no weight on it.

Anyone know what is up with this weird toilet?

If you have a Watts Flood Safe for the water supply, replace with a normal supply tube.

The Watts does not work with most toilets.

If the tank is refilling, check the flapper.

Since 1992, toilets use 1.6 gallons.
The tanks hold 2.5 or more gallons.
Much of the water stays in the tank.
That is normal.