Absolutely an out of combat thing. There would be many occasions where having someone along that could persuade NPC's to cooperate could aid the party. Different classes taking the perk might gain special effects - for instance, a "good" cleric speaking to a "good" NPC might have the opportunity to appeal to their religious beliefs (or guilt) if they had the perk. On the other hand, a persuasive berserker might be one that could threaten and bully someone rather than killing them outright.

And wards would be a lot of fun in so many situations. In fact, more mage-ish classes might enjoy warning wards (for instance, if there had been a ward in the first room in our dungeon we're exploring, we might have had advance warning that something was approaching).

Questionnaire:

1.) What skills/perks would you like to pick from?

Well, that would vary, but I think they should be two distinct things. For instance, clerics might be able to specialize in healing, or in divine smiting. Or they could specialize in an alignment, being good or evil. These would be exclusionary choices. The other type of skills would be generic things that anyone could take - learning another language, or being skilled with machinery, or being a particularly good speaker, or perhaps packing a backpack properly (to enable them to carry an extra item), or pyromania, so they could turn liquor bottles into molotov cocktails. Possibilities are endless, really.

2.) Should certain skills/perks be limited to certain classes, to preserve some character consistency?

Absolutely on the first I mention above. On the second, I think some would be exclusive. For instance, a berserker might not be able to learn a second language. On the other hand, a mage or cleric might never have learned to pack a satchel properly.

3.) How should it be implemented? In other words, how should skills/spells be "earned"?

I'd enjoy a system similar to the Fallout games where a perk could be chosen every level, or every few levels. If they're arranged as perks, they could be specializations OR skills (see above). Even better would be special perks, that you could earn by completing specific goals in missions. For instance, in the campaign the other group just finished, completing the party without entering combat might have earned them a surprise reward (not announced beforehand) of a perk called "Socialite," which gives them the persuasion skill automatically when they are at a formal party or banquet.

4.) Should there be skill/spell "trees" to advance along, and if so, should they be
class-based or not?

Eww, no. Skill trees have been done to death. Some perks might have more advanced versions, but it's far more fun to meet the requirements and go ahead and take a perk you want. Class-based would make sense for some perks, of course.

5.) Should new skills/spells be "static" as they are now. In other words, possible to use over and over again? Or should there be one-time-use abilities?

I don't like static effects. I think they should be ranked in three tiers. Tier one would be simple, obvious things - attacking with a weapon, speaking to someone, or moving. Tier two would be things like a priest casting healing, and they could only perform tier two actions a certain number of times without resting, although they'd have quite a few times they could perform these actions. Tier three might be something incredibly powerful, but a person might be able to perform it only once before resting (say, a priest warding an entire room) and the cooldown would be per ability. This system would make people think before burning out all their healing spells in a single fight (*cough cough* like me *cough cough*).

These are just my thoughts, obviously. I've dabbled in designing a forum RPG before, so you'll forgive my getting carried away - these are just suggestions!