I do use cold water though; it's more convenient and I did not taste a difference tbh.
Also i do not use the wet towel to 'stop the brewing process', I just pour the coffe in my cup as soon as i hear any gurgling.
Can't really explain why, but yes, the original (Bialetti) ones work better than the others.
Coarseness of the grounds should be somewhere between filter-coffee-coarseness and espresso.
I use a gas stove, smallest flame on full power.
When I had a Moka I also used cold water and, like you, didn't notice much of a difference. One thing that I found useful was to remove the pot from the heat as soon as coffee started to hit the upper resevoir.
The thermal mass from the hot water still allows things to brew, but it cooled down quickly enough to prevent that last bit of hot water from pushing the bitter flavours into the coffee. It's worth noting here that I always used espresso grinds in my Moka, for no other reason than I like strong coffee. This method may not be as effective with coarser grinds.
When I had a Moka I also used cold water and, like you, didn't notice much of a difference. One thing that I found useful was to remove the pot from the heat as soon as coffee started to hit the upper resevoir.
The thermal mass from the hot water still allows things to brew, but it cooled down quickly enough to prevent that last bit of hot water from pushing the bitter flavours into the coffee. It's worth noting here that I always used espresso grinds in my Moka, for no other reason than I like strong coffee. This method may not be as effective with coarser grinds.