Wire 6V power packs in series and still use them as individual power sources

Preamble:

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".

Answers:

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.

More soon.
Worst case.

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.

BUT, Best

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 ...

Added comments:

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.

Connecting cells in parallel is common practise with professional battery pack manufacturers, so there is nothing wrong with it. What pros do is they assemble packs from cells out of the same box (same shipment, same lot), having very tight tolerances. This way, you even get packs with serially connected cells (eg. 3s1p) where the cell voltages stay closely matched over the lifetime of the pack (several years) - without balancing of course. This is quite a considerable achievement, you can calculate yourself how much self discharge difference the cells can have in order not to have significant unbalancing.

Your case is much simpler (1s2p) so I guess you are using low quality cells. The above is only valid for top quality cells (Panasonic, Samsung etc), a lot of "noname" cells like used in aftermarket camera batteries are just crap. Which cells are you using?