How much does this vary by jurisdiction? I remember the UK has the "MOT test" which I think does rather more than that, but that's just the UK: https://en.wikipedia.org/wiki/MOT_test
The official inspection is different by jurisdiction, the maintenance plan depends on the manufacturer. The inspection and maintenance are different, for example in regular maintenance schedule there is no emissions check, while the inspection does it. The other way around, maintenance includes checks on all fluid level (coolant, brake, washer) while the inspection does not.
Yes, this is the case in most European jurisdictions. UK mandates inspections once per year (starting 3 years after manufacture). There also appears to be a 2014 EU directive (2014/45) that mandates periodic inspections of most cars across EU states at least every 2 years (starting at most 4 years after manufacture).