If you are going to be using Byetta then you do need to tell the DVLA as Byetta can for some cause a rather nasty hypo..
It is likely that the DVLA, will just write back a nice thank you letter, and no changes to your licence necessary but please keep us informed if your medical status changes etc etc..
Yes you do need to inform your insurance company as well, it shouldn't effect your insurance cover at all.. But if you have an accident your insurance company not being made aware of this can void your cover and refuse to pay out!
As to driving, you need to take the same precautions as an insulin user, test before driving, keep hypo kit near to hand etc..
As I said, it's unlikely for either the DVLA or your insurance company to do anything more than note it down, but this will cover your back...