Can I get skills from Prophecies or Nightfall?

I only have factions installed, and was wondering if it were possible to get skills such as, let's say, "Shock" for the elementalist, which is a prophecies skill? If so, how would I go about it?

I really wouldn't like to have to go and buy prophecies for 1 skill. >_<

Nope. You only get to use Factions and Core skills.

What exactly is a "Core" skill, and would Shock be one? How do I tell what skill is a core skill?

Core skills are ones common across each chapter.
http://gw.gamewikis.org/wiki/Skills_...gn#Core_Skills

if you open up your skill window, you can change how things are sorted, attribute, type, campaign, etc. Campaign will break things into lists like Factions, Prophecies, Nightfall, and Core (assuming you have all the games, if you don't, corresponding skills won't be there)

If a skill was "Added in Nightfall", such as "Black Spider Strike" for the assassin, does that mean I HAVE to go into a nightfall area and get it from a skill trainer? Or would it be added to a skill trainer in Factions as well? So far, I can't seem to find the skill I need, and I recently bought Nightfall.

OK, the whole situation:
-to be able to use a skill at all, you must have the appropriate campaign installed. Even if you somehow managed to get access to the skill, the method will fail. For example, if you don't have factions, and find a boss in Nightfall that uses a Factions skill, you won't be able to capture the skill off his corpse - it will be grayed out.

-within a campaign, only certain trainers wil teach certain skills, although each campaign has a trainer that will teach all skills of the campaign (like Dakk in Ember light camp or Michiko in Kaineng city).

-an exception to the above: if a skill is unlocked in PvP, you can learn it from all trainers in the appropriate campaign, not just the ones that usually teach it.

In the specific case you asked about:
Black spider strike is a Nightfall skill. If you bought Nightfall, you can get the skill from the skill trainer in Kamadan. If you gather balthazzar faction and unlock the skill, however, you can get the skill from any skill trainer in Nightfall.