It can take 3,4,5 weeks b4 they fall off and it depends on how big the calf is. I've done hundreds of newborns up to a few 1200 pounders. The bigger they are in general, the longer it takers to fall off. On the one that you asked about hair growing back, I would ck to see if possibly the band broke after a period of time. If the band was put on a small calf and the bag is still visible after 2 months, I would get him in if I could and either think that the band broke or pull off the sack when you have him in.
As far as Tetnus vac is concerned, the proper and correct total protocol would be to give the calf 2 shots. One of anti toxin, which would provide immediate protection that would last up until the vaccine would have time to kick in, so then there it is, the second shot would be the actual vaccination or vaccine product. I personally band almost all of our calves @ day 1, & don't give any shots and most scrotums are gone within a month, some quicker, some longer, but I can honestly say that I have never had to get one back in to work on. I maybe have been very lucky. Now if I'm working on larger cattle, which I do quite a few for friends and neighbors annually, I strongly reccomend giving the anti toxin shot @ least, and tell them that it is their choice as far as the vaccine is concerned. All of the older cattle that I have done have only received one or the other shot. I have seen some older calves get tetanus from banding, but I have also seen calves that the vets work get tetanus also. The best thing would be to give the 2 shots if you're working older cattle. JMO.
The antibiotics that I would treat the calf with would be LA-200 & long acting pen, that way you should only have to treat him once every 3 days. I would make sure to find out if the calf had anti toxin tetanus or the vac. Vac if it wasn't the vac. Good luck. Brent