Is it normal to want to be meticulously clean after sex?

Sometimes it can be a bit sweaty (and sticky) that I have a quick rinse in the shower, but not a scrub.

Of course it's normal. Sex is not referred to as "being dirty" for no reason. Just feel fine about it.

Yes, but make sure you use the same brand of shampoo, soap etc as you have at home. You don't want your wife to get suspicious if you come home smelling different to how you smelled when you left.

Well of course you would feel that way what with being a "working" girl, by washing yourself afterwards you limit the chances of an STD taking hold, though I am sure you have your local clinic on speed dial anyway. Plus this way you are all "freshened" up for the next customer.