Edited 2017 - changed recommended long life storage voltage and added comments on fast charging using some recent systems. RM.
What YOU do as regards several of these questions depends largely on what YOU are trying to achieve or test.
Discharge to cutoff is fully discharged (to whatever remaining % that voltage represents). That's the easy one :-)
Percent dropoff of current in tail sets final % of max possible charged reached. There was a superb table given here within last week or so. Can supply later if you don't find it.
Real Men™ plateau at 4.2V and tail down to 10% or even 5% of the constant current rate. This gets the battery full and knocks the stuffing out of it.
Others terminate the current tail at say 25% of cc value.
Optimum lifetime for ongoing usage is at about the end of the constant current phase. That makes it very easy to locate - charge at specified current until desired max voltage is reached, then charge at constant voltage as desired. Here "desired" is to stop immediately. This is the point at which batteries tend to give significantly longer whole of life mAh of storage without grossly reducing mAh capacity per cycle. This is liable to be the point where older "fast chargers" tell you they have finished. Actual % total claimed varies but probably 70% - 80% range.
Newer USB input fast chargers use the term differently. In the case of USB the maximum available charge current at 5V is 5A so that the battery MAY be able to be charged at ~= 6A for the CC part of the cycle using an efficient buck converter to drop voltage and raise current.
[For a buck converter: Vout x Iout = Vin x Iin x efficiency_of_conversion]
Some systems such as QuaqlComms Quick Charge system allow the use of higher charger voltages (9, 12, 20) with specifically designed equipment, so battery charging can be faster for a given voltage provided that the battery specification allows this.
Maximum charge rates for LiIon and LiPo batteries are usually C/1 = 1A per Ah of battery capacity.
At 5V, 5A a USB charger can charge a 6000 mAh 1 cell LiPO battery at max rate - so eg a 10,000 mAh single cell battery used in some larger tablets can not be charged at the allowed 10A ! rate.
For long life storage where actual stored capacity is unimportant, LiIon and LiPo cells should be stored at about 3.7V.
Using cells without protection adds to the rich tapestry of life. As long as you don't mind the occasional scorch mark on the tapestry that's fine. Note that part of the protection is a one time high capacity fuse under the cap for when things get out of control. Undervoltage discharge destroys. Charging from below a certain voltage at full rate can get fun, I'm told. Charging at reduced rate can bring cell up, I'm told. Below another second level they say don't even think about it. I've had very poor success in trying to get LiIon to misbehave. I have a box of unprotected cells that are very uncooperative about venting with lame etc. Strange. Sony and Apple and even HP seem to be much better at it :-).
I'll assume a standard Lithium Ion (LiIon ) battery tyoe as used in the very large majority of laptops and similar equipment. Lithium Polymer (LiPo) is for practical purposes the same.
Lithium Ferro Phosphate (LiFePO4) is of the same family as LiIon but has some fundamental differences which mean these nswers apply only partially. I may comment on LiFePO4 separately.
I'll assume "normal" ambient conditions - say about 10C to 35C unless otherwise noted. I may comment on results out of that range.
I'll assume the battery (or cell) has not been deep discharged below the normally recommended minimum discharge level. All well designed equipment will not allow deep discharge below minimum recommended level. This can cause battery damage or destruction and special care is needed to recover a battery from that condition, if it is possible. I may comment on that at the end.
I will tend to use the term "battery" to mean cell or battery (= N cells) when the text applies to either. If I mean 1 cell specifically I will use "cell".
Force charging-Charging even after reaching 100% in battery backup.
- You cannot "force charge" a LiIon cell as long as you do not exceed design parameters of maximum charge rate and maximum charging terminal voltage. The battery is normally charged at design current until maximum terminal voltage is reached and then allowed to accept whatever current the chemistry involved desires until a cutoff point is reached.
Two parameters that affect life and charge capacit are the maximum terminal voltage used and the % of maximum current that you allow the current to fall to before you terminate charging. Reducing maximum terminal voltage and/or limiting that the current falls by before charging is terminated will increase cell life, at the expense of storage capacity in both cases.
Here is an immensely informative chart, care of Battery University, that tabulates the affect on capacity of various endpoint voltages and charging cutoff point. eg the traditional maximum charge voltage is 4.2V. When this cell voltage is reached the cell has 85% or maximum capacity. If charging is at 1C hen this occurs in about 85% x 1 hour =~ 50 minutes. If charging is allowed to continue for another 180-50 = 230 minutes the capacity will be 100% and charge current will be close to zero - say maybe 1% of max. Leaving the charger connected will have minimal additional effect. Disconnecting the charger when 4.2V is first reached will reduce available capacity by 15% BUT will increase cell lifetime by much more than 15%.
Charging only after the battery empty.
Better to charge little and often with battery more full.
Recharging back to point of 1st reaching 4.2V is best.
Charging parallel while working.
Good. Charger may charge battery plus operate computer if of enough capacity - this is almost always the case with chargers supplied with the computer. If not, it will slow down the discharge rate.
Charge to cutoff voltage as per table above.
Disconnect battery and operate computer from mains supply.
This is the best point to maintain the battery at.
Battery will achieve maximum calendar life.
More on the above plus other comments later probably ...
Manufacturers tend to produce chargers which achieve close to maximum capacity. This gives longer operating life which assists the "consumer experience" [tm].
It also much shortens the available battery cycle life which is not so noticeable to users. This increases the number of batteries needing to be bought at accessory level prices during the equipment lifetime. This enhances ghe manufacturer and reseller experience :-).
While it would be possible for manufacturers to stop charging at less than complete capacity, and while some may truncate charging somewhat early in the final "current taper" part of the charging cycle, the majority dio not reduce capacity as much as is desirable for long life.
The OLPC laptops use either LiFePO4 or NimH cells. By limiting NimH charge and discharge to not include the top 10% and bottom 10% of capacity they get 2000 cycles from a NimH cell !!! LiIon can be extended by such methods.
Best cycle life a a given end-point voltage is achieved by stopping charging when the voltage "pedestal" is reached. As per the above table this gives 85% capacity at Vpedestal = 4.2V, and 75% at Vpedestal = 4.0V.
Batteries when unused last longest when stored at the end of constant current / start of constant voltage point.
Charging while working was covered above. Stopping the battery discharging further is a major gain. Extremely high temperature is not tolerated wll by LiIn cells but temperatures to about 40C are tolerable with no great problem.
What the extra bit of information means is that to realize the full 6600mAh capacity of the battery you would have to limit the discharge rate to 1320mA. That gives a typical usage time of 5 hours at that load.
When you increase the discharge rate you will change several things.