Is it safe to unplug a li-ion battery not-discharged and leave it unplugged for a considerable period of time? (Less than a month)
Is it safe to unplug the battery while the PC is on and directly plugged to an AC power?
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What you should not do is leave a Li-Ion battery sitting in an uncharged state for long periods of time. Li-Ion batteries do not do well if left uncharged for long periods of time (though they also do not do well if kept constantly at full charge either).
Also, you generally should not remove the battery from a laptop (except to service one or the other). Even though it's plugged in, most laptops still draw on the battery from time to time for "peak" power needs, and hence they will be "throttled" (slower) when running without the battery in place.
As of Wikipedia the self discharge rates are:
8% at 21 °C
15% at 40 °C
31% at 60 °C
actually leaving a Li-Ion battery for a 'short' long periods of time, such as a Month, i don't think it would cause a problem since i have a lot of batteries left for more than a month and they are still working
actually the only problem you may face is that if the battery got flat to around 0 Volts, the Laptop/Device may not be able to detect because the battery circuit can't turn on, also it may damage the battery it self as what happened to my Laptop battery, it caused the Circuit to reset it's memory and made my laptop say that the battery isn't original
if it's a normal battery and not those Laptop batteries (Without a Circuit), you may be able to charge it slowly until it reaches the needed voltage and then it can be re-charged
And about unplugging the battery from the laptop and 'Force' a shutdown will not cause any problem to the machine, except the HDD, you may loose some recently copied files and the OS may get damaged
However, if you have a Windows OS, you Can Turn off Disk Caching from Device manager to prevent data loss
EDIT: I'm sorry i didn't know that you meant to unplug the battery while AC is connected, for that, you won't have ANY Trouble of any kind at all, if you have Windows, then it will tell you that no Battery is detected, you can plug/unplug the battery at any time while Connected to AC, the Laptop won't shutdown though.
I will leave the above information's for anyone who ever had this question.