Hello, and thanks for your question!!
Depending on the age of your toilet, you may need to replace the seat where the flapper sits. The plastic will corrode over time and cause very tiny cracks and scars where the flapper sits. This is going to allow water to get through and then trigger the fill valve. A very simple trick to find out if that is the problem is to drain the tank, apply Vaseline or plumbers grease to the flapper seat and set the flapper back on to it and fill the tank. If the problem slows down or goes away then you know that you need to replace the flapper seat.
If it still happens then I would replace the fill valve.
I hope this answers your question, If not im still here to assist you.
If the vaseline works and I therefore should replace the flapper seat, is that something easy that I could do? How do I do that?
If the vaseline doesn't work and I therefor should replace the fill valve, do you mean just the fill valve or the whole Fluidmaster 400 thing?
If it the seat, you will need to remove the tank from the toilet. This can be tricky if the toilet is old because the bolts and such corrode and rust. Overall its not that hard. Removal of the tanks is the hardest part. once you remove the bolts, the tank will just lift off the bowl. The seat has 3-4 parts depending on the brand. The parts go together in series as to make the tank/bowl connection water tight.
The seat assembly inserts into a rubber washer then into the hole of the tank, a plastic nut will then secure the parts together. You will also need to replace the soft rubber gasket/bushing that goes between the tank and bowl that keeps water from leaking at that location when the toilet is flushed.
If needed, I would just replace the whole flush kit, It comes as a unit and is inexpensive.
Thanks again, Charles