Literally, 1G means "one grain" and 2G means "two grains", etc. For Aerotech 38mm hardware, the case that holds only one grain is in fact the 30/120 which delivers an average 120 N-s impulse. This varies somewhat with propellent formulation. In 54mm diameter, a 1G case would produce higher impulse. For 38mm Aerotech reloads, your translation is correct and I assume that other manufacturers would be similar.
You're pretty much right. Aerotech and Cesaroni cases follow roughly the same grain and case sizes.
For both AT and Cesaroni 29mm cases, each added grain = 60Ns, except for the 29/100 case which is weird, and the Pro29 6GXL case which is also weird.
For 38mm cases, it's roughly 120 Ns per grain for the Aerotech cases, and a tad more for the Cesaroni cases - more like 140Ns per grain.
54mm: AT 426Ns per grain, Cesaroni around the same.
75mm: AT 1280Ns per grain, Cesaroni around the same.
98mm: AT 2560Ns per grain, Cesaroni the same.
Note, though, that those are roughly the maximum impulses per grain, with an Isp of 200+ seconds. Blue propellants and stuff like Warp Nine and Imax are right around the maximum for the propellant grains, whereas Black Jack and Skidmarks get only about 2/3 of that maximum.