Do you have a proper contract drawn up with them? Legal and binding and all that? How much notice they need to give and vice versa?
I think its odd they keep calling you to explain their bills. Its not difficult to set up direct debits to pay regular ones, which would be the easiest thing for them to do. You should not need to be involved.
With regard to them maybe not paying bills and moving, I'd be inclined to get legal advice on that as you as the home owner may be stuck with things if they do leave unpaid bills and move. Although they should get their act together and notify all the companies to come do final readings etc when they know they are leaving and have any outstanding bills sent to their new address. You can call the council and enquire about the process for council tax also with regards to your tenants. The council should not stick you with that unless the property is empty. But worth calling and finding out as thats not a cheap one either.
Failing that, I'd install a key meter for electric as that tends to be the big one if left unpaid. At least with a key meter they have to top it up themselves or else have no power. Make them responsible for it.
Might pay you to seek legal advice and if you know these people are leaving, you phone all the utility companies and double check the process? Not sure they will tell you anything as you are not the bill payer, but its worth a shot.
It really sounds like your tenants need to learn to fend for themselves a bit though. Its not your job to help explain their bills or to have to become involved in anything like that. I'd be inclined to keep more of a distance but thats just me.
Good luck