Re: Cistern overflow!
This sounds like the same problem I had with my modern flush toilets and it's very common TBH. The symptom was water constantly trickling into the pan after flushing.
The cause was simply the flush mechanism which amounts to just a metal cable behind the push button. When you push the flush button the cable moves a lever down in the gubbins inside the reservoir. That cable and the lever just get gunked up over time. The lever has a spring on it which is supposed to bring the lever back into position when you release the flush button but when the cable gets a bit rusty and gunked up that spring isn't strong enough and so the lever stays partly in the open position which means water keeps trickling into the pan.
The fix was really very simple, for me at least. The "gubbins" in the reservoir was just a plastic cylinder which was removed with a simple twist. The cap came off revealing the point where the flush cable met the plastic lever. You could press the flush button and see the lever move and make a central piece of the mechanism rise and fall. I just cleaned the lever and cable end, sprayed some WD40 in there, added a little bit of grease so it moved easily, and then I added a small weight to the central moving piece that went up and down. That fixed the problem. To be fair you could probably achieve the fix just by putting the weight on the moving part so that it always shuts off the water.
These modern flush systems are quite tickle really but they look neater than the old crank handles of course.