Unlocking Skills From a Campaign You Don't Own

Is it possible to unlock or acquire skills from a campaign that you don't own? I mean I only have Prophecies and EotN, but what happens when I unlock my non-core profession heroes in EotN? Do their skills get unlocked? Thanks in advance.

no

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So will my non-core profession heroes not have any skills?

They can use EotN skills of their profession, plus skills of their secondary.

Heroes come with 4 or 5 basic skills, then as Nyktos said, they can use secondary profession skills.

You can also get new skills from Hero Skill Trainer NPCs.
http://wiki.guildwars.com/wiki/Hero_Skill_Trainer

So I can use those 4 or 5 basic skills on that hero even though those skills are from another campaign? If so, then can I also use those 4 or 5 skills on my other heroes' secondary professions?

Heroes can use skills from campaigns you don't own, however should you take control of the heroes skills by opening their skillbar, you will not be able to activate those skills.