You can use a wheelie bin fit out with filters and valves etc. I bought one a few years back from Malcleanse but not sure he sells them now. Should be easy enough to make your own. Plus point is that it's easily mobile and you can store lots in it between job.
99% of the time on domestics connecting to their supply isn't a problem. Occasionally low pressure is a painn so one to be mindful of when quoting as this can quadruple the time spent on a job so alternative supply will be required. If you want to draw straight from the main you'll need to arrange with your local water authority, this isn't cheap.
Yep, driving on is fine, you should only be taking the top bit of jointing sand out when you clean so blocks will still be solid. It is important to identify any 'weak' areas before you clean and point these out to the owner. Raised edges are a common area as are dips due to poor workmanship and even ants nests, anything where the joints have a wider gap usually means problems.
Finally, don't leave too long after washing to resanding etc. as you'll cause yourself loads of extra work, espeically with clay as the joints get full of all sorts of crap which will need to be cleaned out prior to sanding.