I've been told in the past that you cannot outwit a team ability. I have some fresh meat in my playing circle and they have recently asked the "why not" question. Exploring the FAQs, I couldn't find one that applied (if team abilities are considered "powers"). Also, I don't think any of the FAQs have addressed whether feat cards can be outwitted. If so, the power of outwit became much more desirable. So my questions are:
1. Can team abilities be outwitted?
2. Can powers gained by feat cards be outwitted?

From the Universe PAC:
OUTWIT (optional): Once during your turn, as a free action, this character may counter a power on a target opposing character. Treat the target as if it does not have the countered power. That power remains countered until the beginning of your next turn. This character must be within 10 squares of the target and have
a clear line of fire to the target. Instead of a power, you may choose to counter an opposing flying character’s ability to soar; in this case, lower the soaring character to hovering mode. If this character loses Outwit or is KOd, the countered power returns immediately. You must declare that this ability is being used before rolling to hit.

So we see that we can counter Powers and Soaring. Meanwhile from the Universe Rule Book (pages 12 and 13):
Team Abilities
The colored symbol on a character’s base indicates the character’s team association. Teams have special abilities that their members can use. Team abilities are described on the Powers and Abilities Card. In general, a team ability is in effect as long as one member of that team on your force is still on the map, though some team abilities require that more than one member of that team on your force remain on the map. All team abilities are optional. Some characters or versions of characters have no team affiliations. Team abilities may not be lost or countered.

The only exception to that rule is the BFC Disbanded! which specifically states that all TAs are ignored.

Now for your second question: if a card specifically grants a Power (such as the Toughness granted by Force Field, or Perplex from using the second part of In Contact With Oracle), then you may Outwit that Power. When a Power is granted, it is essentially on the character's dial, along with any other Powers the character has and is subject to Outwit. Other abilites that aren't actually Powers, (such as Haymaker's +2 to Damage) may not be Outwitted; they aren't Powers and we already eastablished up in the first part that Outwit works on Powers and the Soaring.

Does this help?

1. No. They cannot. Team abilities are team abilities. Outwit only works on powers. However, powers granted by a team ability (Like Probability Control from CSA) can be Outwitted.

2. Yes, Powers granted from feat cards can be outwitted. For example, Toughness can be outwitted on a figure with Forcefield. Of course, it's smarter to outwit the pre-req, provided the piece only has one showing...

1) I know that TA's cannot be outwitted, but I'm pretty sure powers (such as Outwit from Batman enemy and Prob Control from CSA) can be outwitted.

2) I am pretty sure that Feats cannot be outwitted, but prerequesite powers can. so theoretically you could outwit feats like pounce, auto regen, and damage field by outwitting leap/climb, regen, and any of the damage field prerequsites.