As you say, it is impossible to know for certain. Having a visa is not infallible, and it's not a guarantee - that applies to any country.
If you were questioned heavily, as I and many others have been in recent months, the decision as to how seriously you treat this red flag is entirely yours, but it IS a red flag.
You need to start pushing the school to do its job and guide you through this. If they are letting you flail around guessing that you can use a 15 year-old police check then they could seriously mess you about later on. I know they probably brushed you off and said "go do on website" but they have a responsibility to guide you through this.
For clarity they won't be "attaching a work permit" at all. That is a subsequent step (through the labor office) once you have the Non-B, and THEN you can legally work.
All airlines go by today's rules as in force today. This was the same all through the frequent covid changes Obvious reason being that governments can backtrack.
Tourist visas in neighbouring countries is getting harder to get. Check the specific local requirements extremely carefully. In any case, a tourist visa is not a magic wand for entry. The denied entry is in the system.