Skill-up's

[Reynhart]

No
Class exp was for your class, not for your skill.
You got class exp and physic exp. The physic exp was for your char (mostly for stats). If you leveled a class but not the char (don't got new stats) your skills didn't level up. Class exp was mostly for quests, equip and skills (to learn them, not to make them stronger).

Wrong.
Skills were based on you class rank, not your physical level.
So if you gained skill points for you class, you learned new skills, even if your physical level stayed the same.
The only impact of physical level on your skills was the number of action points you had.