Lithium-ion batteries explosion risks and storage/usage rules
Clarifications


  It is a good practice to not let your device discharge to levels less than 20% and avoid deep discharges


Many devices like cell phones limit battery usage between 20%-80% SOC to get the longest lifespan, and remap that range as 0-100% for the user.


  Do not overcharge battery and don't charge it with very high currents.


You can charge with "high" currents. It all depends on the cells you have. In general the higher the charge current, the shorter the lifespan of your cells will be.


  Cold temperature


It's not that it discharges faster, less of the electrochemical energy is available, as the reaction that produces the electricity is inhibited by the low temperature. Once the cell warms up it's able to function normally.


  Best condition is to store Li-ion batteries at a charge level of about 40% in a dry cool place


Sounds about right, it's a common choice for storage SOC. As for their self discharge, get a storage charger that will top them up once in a while or just remember to do it yourself. Their leakage isn't huge, I've left packs sitting for many months at storage charge which are still fine. Your mileage may vary.


  
  I rly wonder if a properly stored battery can explode by itself in certain circumstances?
  


No, something has to go wrong with the cell. Usually physical damage.


  
  Is it safe to store old deeply discharged batteries at home, or there is a risk of accidental explosion and they should be re-cycled as soon as possible. 
  


If they're very discharged there's little to no risk of explosion.

Cells explode due to heat, usually generated by an internal short circuit or just having way too much current pass through them. If they're deeply discharged there's no energy stored to convert into heat.