is this 25 cal as quiet as the specs say?
Yes, very quiet
Now how exactly do you recharge the tank on this air rifle. can you specify more the PUMP? Does it need a pump to recharge? Can the tank be recharged like all pcp tanks?
Either a high pressure tank or a hand pump can recharge the gun, just a matter of having the right adapters.
would be ok to use compressed Nitrogen as the gas for my Hatsan AT44
What does hatsan mean by pump action like hand pump or like a built in pump?
Uses a pump handle to advance the clip to the next round. There is no bolt in this design. Look at the images and you'll see it.
You do not have to engage safety after every pump, correct?
It does have a manual safety, so yes you would need to engage it. You can see a link to the manual in the description tab that outlines this procedure.
Wish they would offer this gun in a QE version with the thumb hole.
This IS the QE version. Maybe it wasn't when the question was 1st asked.
Unfortunately it's not available at this time