1.) If I give a follower a weapon with Soul Trap, and then give them soul gems, will they be able to take souls?

2.) The Recovery perk in Restoration (Magicka regen), does that make your magicka regen faster in combat, or just outside of combat?

From the Wiki :
"Giving a follower empty soul gems and equipping them with a weapon enchanted with Soul Trap can help to fill souls easier, freeing the player up to use other enchanted weaponry."

In combat, but 50% of a lot less is a lot less. Normal regen is 3%/second of your total outside, .99% in combat. so regeneration perks will give about 1.5%, unless you are holding a spell ready, when it's 0% either way.

Okay thanks for that.

If that's the case, then I won't worry about taking those perks, as I'm not worried about outside combat magicka regen.

Yeah, it's not a lot. I only take them to offset the -50% from the Atronach stone.

If you put numbers to it, say you are a level 21 breton spellsword, with half health, half magicka, for 200 points, no stone of other regen effects. You regenerate (about) 2 points a second without the perks, 3 with both. Independent of your actual amount, that's a minute forty without potions or the like to fully regen from 0 in combat, one minute 7 seconds with the two ranks. Add in, say, Robes of Expert Destruction (+125%), 4.5 points a second without, 5.5 with, or, again independent of your actual amount of magicka, 44.5 seconds without to fully regen, about 36.5 with the perks

Thanks for your responses. Definitely helped me out to better utilize my limited perks.

1) Yes.

2) It affects both, inside and out of combat.