No-answers-found Li-Ion battery questions Background
I've spent almost 7 hours researching about Li-ion batteries because my Galaxy S2 only lasts 2 hours with all turned off and only 40 apps installed (removed system apps and bloatware) and screen brightness below lowest normally possible in settings (I use ScreenFilter and set its opacity to >80% which means the slider is at less than 20% and I can barely see anything) when playing not CPU stressing game or just installing and removing apps and setting settings!
Questions not answered yet after almost 7 hours of searching
After putting battery in freezer overnight (in ziplock bag to avoid moisture (according to sites battery loses >20% Capacity in >3 months to a year) ** does the rapid heating up cause by turning phone on and games harm battery?**
Exactly how much is it safe to discharge?
(I've found to avoid full discharge on several sites but no site says exactly how much of a discharge isn't harmful except about 20% but with no sources to back it up and I don't know how accurate is that "about")
Why does my phone discharge so fast? (2hours even when not gaming; see background)
 A: There are two options: your system is drawing to much power or your battery capacity is getting low. Assuming you limited the first, it leads to the second.
Batteries have finite lifespan. Batteries are consumables. How many times have you discharged the cell, about 500 or 1000 times? More important, in which conditions? Has the cell overheated? 
It is impossible to diagnose what your cell exactly got without analysing current rating curve and charge/discharge curve.
Anyway, capacity loss happens because of chemical process irreversibilities (lattice deconstruction, channelling, passivation) and design imperfections (aimed or not). Those problems generally get worse when temperature increase (think over many cycles). But it does not mean you can recover from them by freezing the cell! This is why it is called irreversibility: you cannot reverse it by walking back through the same path in opposite direction.
You will not be able to operate your cell phone bellow ~15% of full charge of the battery (this ratio might not be the one displayed) because beyond this point delivered potential dramatically falls and the cell cannot provide the required 3.3V to feed the phone chipset.
