In oblivion there where major skills and only those increases counted towards next level. Is it the same here or does all skills - regardless of race - counts toward level increase ?

Yes. The higher the skill level, the more experience it provides.

This is the change that surprised me when I read it in the manual.

It is no longer a base total 10 skill levels to level your character. It feels like leveling a high skill will level you faster. Interesting change.

Yes an interesting change and much better than Oblivions levelling system.

That is exactly right. Basically, say you are level 20, and you level One-Handed up from 50-51, it will provide much more experience toward the next level than levelling, say, Enchanting up from 15-16.

I really like the change, because now everything you do truly adds to your character.

Yes they do.