Ginger beer is an odd brew, there are is seems two organisms used in the brewing one which produces alcohol and the other which feeds on the alcohol so the end result is not alcoholic. I remember the so called Ginger beer plant, adding sugar and ginger daily and after 14 days straining the liquid off and diluting and bottling splitting yeast into two plants and starting again. Unless swing top bottles were used which auto release the pressure bottle bombs were common. But in spite of all the sugar added one could drink the brew as a 6 year old and it did not make me drunk in any way even after many glasses of it. It seems the original Ginger Beer Plant containing the yeast and bacterium Zygosaccharomyces florentinus and Brevibacterium vermiforme the latter two remove the alcohol.
The use of a hydrometer does nothing, one as the yeast and sugar is added daily and two as it will show a ABV which is erroneous because of the bacterium. Although there are sites offering the plant the yeast and bacteria are naturally in the air, so it is easy for any ginger beer to gain the bacteria and become non alcoholic. I made some coopers alcoholic ginger beer, and after storing it seems to have lost it's alcohol, it was never as high as instructions claimed, it should have been around 4.5% ABV but it did not have the effect of a normal 4.5% ABV Bitter Beer. The bottles pressurised, then the pressure went, and every bottle the same, all PET bottles and although one cap may have been loose not every one was loose. So two years latter really ready to pour down the drain, but a Bitter beer is still good.
As to labels I use simple Sellotape to stick them onto the bottle, I print with laser printer so label will not run, and important bits covered with the Sellotape as found other wise the slugs and snails eat the labels when stored in the shed, seems they also like beer.