Getting car repair for minor rear end

In a parking lot, some car tapped my car from behind while in slow speed (<10mph)

There's no visible damage to car bumper. The other party's insurance contacted me.

1. Should I still go and get the car diagnosed for internal damage? Will it play a role on my car's carfax report ?

2. I had carseat (and baby) inside. Should I replace ?

3. We didn't feel much impact, but should we still get it checked?