If they've gone below 3V with self discharge then they've probably been left that way for a long time (which is a bad thing).@ZOR I have used some OLD lithium cells from laptop packs - some of them have very LOW self discharge and others not - so if you go that route better test - in any case it is apparently unhealthy for them to go below 3v or so with a load [not sure about self discharge].
Hmm... yes it does happen. My neighbour three houses away suffered a lithium-ion battery fire late last year and they only recently completed the repairs to the property. They spent a night in hospital following smoke inhalation and the fire brigade visited all the houses in the road warning of the dangers of charging lithium-ion batteries. I usually charge mine in the stainless-steel protection of a kitchen sink, just in case. The problem is that we have so many of these devices around these days. I note that the instructions for the pack that Hippy refers to states; "It is normal for Juice Bank to become warm during use. Stop charging if it becomes excessively hot. " - and just how you spot the overheating when you are tucked up in bed whilst the things are charging is beyond me! The same sheet instructs; "Do not attempt to charge and discharge at the same time"- which answers another of your questions. More importantly, it continues; "In the unlikely event of a fire, douse the flames by submersing in water (e.g. a bucket of water)". Well, yes, we all keep a bucket of water nearby when charging Lithium Ion battery packs, don't we? Remember the problems that Boeing suffered with the Dreamliner and Lithium Ion battery packs which went into thermal runaway and caused substantial damage to several airliners.Hippy: I had a quick look for the lithium battery packs you mention but do you have any links to battery and charger. I have been treading carefully on these battery types with the publicity around them of fires and exploding. In addition reading about cheap Chinese batteries being risky.
Perhaps no one here knows or is not willing to make a definitive statement which you or others may later rely upon. No one will want to say "yes, you can do that" and then find out they were wrong.No answer came back on this