1) That's not "fast" charging. The normal max charge rate for lithium batteries is 1C - which means that if the phone can accept enough current you can fully charge a battery from 0.1% to 100% in 1 hour (plus inefficiency - no energy conversion process is 100% efficient in a universe with entropy), so 1.5 hours for an almost full charge (from 15%, not from fully discharged) is a normal charge rate. A fast charge would be 15 minutes - which is just a way to increase the sales of new batteries. It may be nice to be able to get 8 hours of charge into the battery in 15 minutes, but unless the battery is rated at 4 times the power that the phone uses in 8 hours (which would be about 12,000 mAh in most phones), it's cooking the battery into an early grave.
The Nanyang Technological University in Singapore recently (last month) announced a different lithium technology that allows very rapid charging, but as of now a) the battery to power a cellphone would be MUCH larger than a cellphone and 2) it would cost more than the most expensive cellphone. (And, given that the life expectancy is about 20 years, it probably will never see the inside of a cellphone - it's being developed for electric cars).
2) When the phone says 100%, the battery may or not be at exactly 100% charge. The phone estimates the state of charge by the voltage, which is about the most inaccurate way to do it - but it's cheap. (Only a chemical analysis of the battery - after taking it apart, which destroys it - can tell you the exact state of charge.) Let it charge until it indicates 100%. Then let it sit without charging for about 5 minutes. Then charge it again for 15 minutes. (It should actually sit for 24 hours before charging - but the fact that reality isn't very practical doesn't alter reality, and no one is going to sit with a dead battery for 24 hours every time the battery needs charging.)
3) Letting the battery run down to 15% on rare occasions is okay - it won't impact much on the life of the battery - but for maximum battery life it should be charged when it's down to about 40%-60%.
Battery University - How to Prolong Lithium-based Batteries.
Facebook
Twitter
Instagram