Let's assume we have a level 10 Arcanist, who has taken the School Understanding exploit, and chose the Air School. This will get her the Air Supremacy feature from the Air School.
I'm fairly sure that without using any arcane points, the arcanist would now be able to cast feather fall on herself at will.
Where I'm less sure, is that if she uses an arcanist point, can she now cast fly on herself at any point for the next minute? And presumably that fly spell would last for 10 minutes.
Yes, you'd get Feather Fall at will, since that's granted at level one with the school.
And as long as you've used the Arcane Point to treat your Arcanist level as your Wizard level, then yes, you gain all the benefits. Including casting Fly at will. And since it doesn't specify any changes to the normal duration, it would last 10 minutes per level, since you had a caster level equal to your level when you cast it.