I agree with your interpretations. The fact that Nils Bargren a couple of times was called Hans Bargren was probably only a mistake. There is quite a lot of examples of that in the parish registers.
Nils patronymic was Hansson. In the military enlistment rolls is Nils always called Nils Hansson Bargren. He was enrolled 1719 and he was from the province of Skåne in south Sweden. He was 30 years old 1722, 34 years old 1726 and so on so he must have been born around 1682.
There are lists from 1721, 1722, 1726, 1728, 1732, 1735, 1737, 1740, 1741 and 1745. In all lists except the one from 1745 he is called Nils Hansson Bargren. In the list of 1745 he is called Erich Hansson Bargren and it also gives the information that he was dead in Fredrikshamn 18/2 1742. But it must be the same person. Again an example of when the scriber has written the wrong name, maybe understandable three years after the person died.
Livgardet (the Life Guards) was a recruited regiment and the soldiers came from all parts of Sweden.
When I googled Bargren on swedish sites I found two other Bargren/Bahrgren around 1750. Both were soldiers in Skåne.
In Skåne there is a parish Bara. Perhaps these soldiers have origins from Bara parish?