Error...?

In guildwiki, under the skill "Hex Breaker", it says that it can obtained in Nightfall through Tohn, who is located in Kamadan. However, I've talked to him and he won't teach me the skill. It's listed as a core skills, so how would I learn it in Nightfall. Also, when you purchase a skill for one of your heros, does it also become unlocked for your PvP characters, or do you actually have to go become the class you wnat skills for?

GuildWiki is not always right. No idea whether or not it's mistaken in this instance, but as to your other question, the method you use to unlock does not matter. Once a skill is unlocked, in whatever fashion, you are free to use it on all PvP characters and heroes of all characters on that account.

By the way, core skills are common to all chapters, and can thus be learned in all of them.

edit: according to wiki's page on Hex Breaker, you can acquire that skill from Warden of Whispers in Chantry of Secrets, or from Zendeht in Gate of Torment, but not from Kamadan.

Yes. If you want [[hex breaker] you must be a Mesmer primary or secondary to see it listed by skill trainers.

Tohn DOES have it, I unlocked it there when I bought it on my Mesmer.

Just make sure you switch to /Me if you're not a Mesmer primary, and look carefully at all the skills - use the name list if you don't recognize the icons easily.

Alternatively, you can get it in Factions as early as Seitung Harbor or Kaineng if your NF character get get there. Or simply have another character buy it, so it's unlocked, and then you can use a tome or buy it from any skill trainer.