additional pix - hope they are an improvement for seeing the profile. In couple of them the internal tubular hole can be seen running down inside the handle, though still not clued up as to the reason for the hole, or come to that how it's achieved - you can see the pipe cleaner in the hole, and I'd guess the hole is c. 5 - 6 mm diameter. Visually, would look v.g. if the jug was filled with red wine or beer, but with water the effect is lost, though the whole point of the hole may not be for aesthetics.
Not being clued up at all with such pieces, I've no idea as to suggesting which design came first - those with the strap handle or this hole in the handl job - or whether both were concurrent. In fact not sure what date to suggest - 1940s?
Traditionally, cut/finished at the top has been the Continental method, with solid pontil rods a U.K. preference, but as with all things no doubt there are exceptions.
I've seen a lot of crackle style glass, in many forms and shapes, but don't recall ever seeing label let alone a backstamp, so no idea if there is a single predominant country/source.