Is skills unlock permanent?

I have 3 toons: E/Me, Mo/N and R/W. Now they are all at droknar's forge.

As I understand we can change the 2nd professions at gorge. I really want to change my R/W to R/E, so I could use barrage and conjure flames.

If I made the change, I guess I have to redo all skill quests to get E skills, but what happens to the W skills I already unlocked?

PERMANENT UNLOCK EVEN IF TOON DELETED

it is account based not per character

Actually, to change to Elementalists you need to go to Heros Audience.

* Seeker's Passage - Monk / Ranger
* Hero's Audience - Necromancer / Elementalist
* Destiny's Gorge - Warrior / Mesmer

You don't have to do all of the Elementalists quests to get the skills. Most of the Skill Traders in the normal areas, like Ascalon, Yaks Bend, Lions Arch will have most of the skills you want. Only certain unique spells will require the search for the skill trader, like Meteor Shower is traded in Ascalon Settlement, so you'd have to make the journey there. Look up the skills here in the Skill Listing Guide, and find out who the skill trader is for the skill then go purchase it from them.