If Li-Ion battery is deeply discharged, is it harmful for it to remain in this state unused?
No, it is not OK to have a Li-Ion deeply discharged at all.

Here is why:
When discharged below its safe low voltage (exact number different between manufacturers) some of the copper in the anode copper current collector (a part of the battery) can dissolve into the electrolyte. The copper ions (atoms?) then in turn can stick on to the anode during charging by chemical reduction and cause dendrites. The dendrites might cause a short circuit inside the battery. So basically discharging too much is as bad as charging too much. But the dendrites caused by overcharging is formed out of lithium. 

Normally the battery pack should have some sort of supervisory circuit that disconnects the cells from the charger or load when the cells are above or below  the recommended voltages.

Question 2:


  Does a deeply discharged battery have higher or lower self-discharge compared to normally charged battery?


A deeply discharged battery might have a higher self-discharge due to the above mentioned damage. 

From what I can see in the data sheet provided by a large manufacturer (under NDA) the best relative (%) capacity retained is at somewhere around 50% charge and at low storage temperature.