1) Skill points must be connected to the center to be active. If you rotate and they are no longer linked, they become inactive.
2) That button toggles on the auto-dash mechanic - used for melee to automatically dash into melee range and hit the target, short cooldown.
3) Can't rotate the camera.
4) Numbers green is increasing from what you had before. Sometimes small display bug where it turns red in error. Stats are based on what kind of build you want to make. Ferocity = attack/spell crit, toughness = health, agility = attack/spell speed, wisdom = status ailments. If you wanted to focus on crit spells then you would prioritize ferocity as a mage.
5) Design choice I guess. Don't stress it too much, you'll eventually find all the skills and try them out. Make sure you go into the side areas for more chances at getting skill drops.
6) Catalysts enable hybrid caster/attack builds which largely ignore basic attacks. Cast spells to generate rage, then use attacks to convert back into wisdom. Enables a lot more skill combinations. Various uniques enable spells or skills to bypass the catalyst requirement.