You do need high inteligence to learn higher level spells.
Yes but would like to see "specialized" spells/skills that require more points into certain skill/school for more specialization instead of skill points only allowing you to learn more of a certain school.. don't know if i'm saying it right or not.
You are, thats not a bad idea at all.
It could be one of the possible options to make investing points into any skill actually as valuable as just diversifying into many because current setup of just getting more slots - while you can change the learned skills in them more or less as you please - is to weak as an incentive.