Suspect Car Dealer?

We're in the market for a car from an AutoScout dealer. After much research, that car appears to be a fair price for the mileage, age and model so we made an appointment to visit.

It was raining heavily when we arrived and the dealer seemed a little uninterested and just left us space to walk around and review the car. It was in great condition given it's age, with only minor scratches and a worn front tires. He said he'd do the TuV when we confirm the purchase to maximise the time left.

Red Flag (One)?

We then ask for a test drive and he agrees for us to go alone but asks we return in 10-15, minutes to allow him to go pick-up son who's disabled and needs help in the rain (red flag?). We do, the car seems fine but we're feeling quite rushed and ask to come back at the weekend for more time.

He is find with this and says he will reserve the car for us and doesn't push for a deposit.

Red Flag (Two)?

At home, I can't find any public presence for his dealership (Google listing, company registration, FB page) only a good track record of Autoscout reviews. In does however, he seems to be heavily involved in the community as a president for a local Verein (with photos everywhere).

Am I being overly cautious here or are these indeed red-flags? What else should I be looking for?