It might make sense to add a new cleanout while they are retrieving their equipment, but no, I would not tear up a driveway just for that unless absolutely necessary.1. Does it make sense to do the excavation for purposes of gaining a new cleanout that is a straight run?
My only experience with a camera was after a line had been cleared, so I do not know about that. But no, I would say you are not responsible for their extra time and expense required for retrieving their cable while trying to clear a clog from your line.2. Is it reasonable that I should be responsible for time and expense attributable to retrieving the broken cable? Should the plumber first have run a camera to see what we were dealing with?
No, but that does not mean they now get to twist things around to where it is somehow your fault their cable separated. This all began with a clog needing to be cleared from a line, and you should not have to pay for anything more than that unless you had first been told the initial attempt might not work but would be tried in order to possibly save you the additional expense of doing some digging to add a much-needed cleanout elsewhere. And if they are now saying that is what had been going on all along (thereby trying to justify charging you from here on out without charging you for the initial visit) but you had not been told, I would possibly dismiss them and hire someone else to complete the job unless they are truly apologetic for not having properly informed you of their planned trial and its possible complications in the first place.3. Does it matter that nothing was really explained to me first?