Yup...using a brush and probably no grit guards and it would seem a bit less of a "detail" place and more of a quickie car wash place.
Wash it yourself using a good automotive soap, use a quality polish or wax twice or three times a year, vac it out every now and then and do up the interior at least once a year with 303.
Even the grit in cheap paper towel can scratch the clear...I use at least three old cotton dish cloths and my main micro fiber wash cloth each wash. Two buckets, one with soap, the other changed out often used to rinse the cloth before picking up another load of soapy water.
to answer your questions:
NuFinish makes a scratch remover (its more a scratch hider...its like crack, once you start you can't stop using it)and there are all kinds of buffing compounds and etc. Some waxes even come with minor compounding ability.
I use this stuff, its good...
Toothpaste can even be used. Ask for help at a good auto parts store. My preference is an independent shop but your chain places should be able to help. Not all of the compounds require a machine.
After you get the scrathes out use a polish. This is different than a wax. Again, ask for direction at the auto parts place. Once the polish is on you can let it cure and then wax or not.
I'm slowly switching from the wax/cleaner above over to Rejex (see current thread on that stuff) and once all my panels are polished I doubt I'll wax over them.
And this response is so long because I'm actually waiting for paint to dry, lol.
Got nothing else to do.