It's not arbitrary. Lithium batteries charging uses voltage termination, and the usual cutoff for 100% on lithium-cobalt batteries (so not LiFePO which is not yet widely used on phones) is 4.2 volts. It's the same for all batteries I've ever used or heard about. You can charge it to higher voltages, but basically nobody sane does that as it quickly becomes dangerous, and 4.2 is pretty much the standard voltage.

Yes, but no. There is an absolute number that the circuitry tracks internally. The hardware does several kinds of measurements to count every joule entering or leaving the battery. The system knows exactly how much energy is in the cells.

The arbitrary value is what voltage you stop charging at. You set your maximum cell voltage and stop charging once you reach that voltage AND input current is below a threshold. Once charging is complete, you store the current energy value as the latest full capacity. That value then becomes the 100% mark.

Remember that batteries lose capacity over time. You must continually scale your state of charge percentage to the actual state of the battery.

The final charge voltage is a tradeoff between safety, longevity, and usable capacity. Higher voltages squeeze a few more joules into the cell at the cost of much faster degradation and increased risk of catastrophic failure.

A cycle count figure on lithium cells is pretty much worthless. It depends quite a lot on exactly how you cycle the battery. A 100 to 0% cycle is much, much more damaging that a 100-50% cycle. Higher currents and temperatures degrade the cell faster. Most cell manufacturers I've seen do give cycle counts under specific test conditions, but that's hardly applicable to real use cases.