Hmmmm. First, I've not watched the videos as I've got zero interest in powering my bike with anything other than my own biomechanical power. Anything else, to me, ain't a bike.
The number of charge cycles a battery will withstand depends on the type of battery, the materials, and honestly, what generation that battery is within its battery type. For some batteries it's not unusual to get in excess of 10,000 charge cycles.
Any battery that can be recharged can be recharged with PV (photovoltaic) cells. The needs of the battery and charge cycle determine what PV resources you need. Frankly, though, it'd be better to opt for fuel cells instead of batteries. Fuel cells last much longer than batteries and have much higher energy densities. I was part of a project that designed a sensor platform that would orbit a point on Earth at 70,000 ft or so autonomously for 3-5 years using a semi-closed loop system of PV cells and fuel cells. The platform is under construction.
An even better option than an electric powered bicycle is an electric motorcycle. The technology has advanced pretty damned far. This year's Isle of Man TT will have a class for electric motorcycles.
Looking a bit further down the road, my university just got a lot of money for development of PV cells only nanometers thick. Whether that's tens or hundreds of nanometers, I don't know, but it would likely result in much higher efficiencies and great flexibility.....as in you could wear them. Right now, PV arrays are limited by their quantum efficiency to about 18%, meaning that for every 100 photons that strike the an active site on the array, 18 electrons are ejected.
