Please bear in mind, that I did look up what I could, but for my own clarity and sanity, any redundant answers I may be getting is still welcome.

1. I am putting together a Big Brotherhood deck and love the card Misappropriation. According to what I read, transfering must follow the equip rules of equipment, hence team restrictions, uniqueness and so forth. So I could not equip a power compressor to one of my Brotherhood characters? What if I made the attempt, would the equip attempt be negated and still go in the KO'd pile? Also, using it to transfer it after a Nth metal powers up is legal as well?

2. I play someone in a local gaming store who uses the Devil's Due, Witching Hour, New Blood, Dr. Doom, Blindsided combo to make Dr. Doom really big and beat you in the face. My question revolves around New Blood specifically...

New Blood, Army
Underworld, Character, 2/1, Common
Whenever New Blood becomes stunned, KO it unless you pay 1 endurance.

Devil's Due
Plot Twist, Rare
Ongoing: KO a character you control Put a +1 ATK/+1 DEF counter on target Doom character you control.

So, when NB becomes stunned, the player attempts to KO it to DD, attempting to get around the payment of 1 endurance. Often this would revolve around team attacking, taking down a larger character and then when one is chosen to be stunned, he KO's it and gives Doom his counter. Is this legal, or can it be if the timing is correct? I thought there was no priority during comparison of ATK/DEF? If this goes on the chain after the stun, then does he have to pay the 1 endurance first before he can KO?

3. Behaviour Modification Device, Team-Up
Plot Twist, Common
Choose two different team affiliations among characters you control.
Ongoing: Characters you control that have either of the chosen affiliations have both affiliations.
Discard a Squadron Supreme character card Draw a card, then discard a card. Use this power only once per turn.

I have been using this team up in my solo Squad curve deck in attempt to discard cards faster and go through my deck. I play it, attempting to name two teams. I cannot. I do not get the ongoing abilitiy of team up, but I thought I read somewhere I do get the secondary effect. Is this true if I did not satisfy the first part. Can I even play it if I do not have 2 affiliations?

4. During the draw phase, Political Pressure is a card that can only be played during the draw phase. What if its the first card I draw, can I play it then? Is there a pause between draw phase and when the first player starts to build? If so, does that allow me to play it then? How would such timing be declared in a tournament setting?

5. Are characters who are stunned still retain their team affiliations, specifically when regards to cards like Betrayal? I have one last character ready, and not teamed up when someone plays that on me. Does that mean I have to stun that character as I have no other choice? What about unaffiliated and affiliated characters on the same board, let us say one of each, does that still work?

2. NB is a triggered effect. the effect hits the chain after the attack concludes, so, on the chain is "KO NB or pay 1 END" if you KO NB to DD before the trigger effect resolves, that is fine

3. yes you can flip BMD if you only have 1 team affiliation to use its discard effect. you just dont get any team-up effect

4. no, you draw both cards at the same time (with an exception for something like Night Vision, where you have to reveal both cards that are drawn, and even then you still are drawing both the cards at the same time)

5. yes stunned characters retain thier team affiliations, so you can use betrayal, like you want. Betrayal does not check for unaffiliated characters. (so, if your opponent has 3 Doom characters and an unaffiliated character, he wont have to stun a character due to Betrayal.)

1. You don't have to check uniqueness when transferring, actually---uniqueness is only checked as part of flipping a unique location or resolving the recruit effects of unique characters and equipment. When you transfer, you aren't recruiting. But, like you imagined, you can only transfer Power Compressor to a Brotherhood character if he happens to be named Dr. Doom.

As for your question, though---based on my reading of the rules, it doesn't look like transfering has targeting requirements. So if you really wanted to, I believe you could target a Brotherhood character to transfer Utility Belt to. But on resolution, the game would see that this transfer can't happen, and so it wouldn't occur. It doesn't appear to be KOed, you just won't move it. But if you wanted to get rid of an equipment, you could just use Misappropriation's KO mode anyway.

As for Nth Metal, it's hard to tell what you mean without a bit more detail. If you just want to be able to use Nth Metal more than once a turn, yes, it will trigger any time its trigger is met.

4. Regarding Political Pressure, remember that the draw phase uses the chain like any other. After the resolution of the "draw 2 cards" effect, you can absolutely play a newly-drawn Political Pressure.

5. Just because a lot of new players get confused by Betrayal, a primer. First, like Togorian said, disregard unaffiliated characters entirely; Betrayal only checks your affiliated characters. Now, if there is an affiliation that all of your affiliated characters share, you're fine. But if you can't find an affiliation that all of them have, yes, you'll have to stun someone.

Sorry, but the rules for equipment transfer states that the character being transfered to needs to fufill any equipment restrictions.
Therefore, you cannot transfer a Utility Belt to a Brotherhood character.

Thanks for all the quick and informative responses. Now I can take this to my game tonight and be confident in my answers.

Twanbon, nowhere in my post did I say that you would be able to attach Utility Belt to a Brotherhood character---I said that it seemed legal to target Utility Belt and a Brotherhood character when using Misappropriation. As I said directly in the paragraph you quoted, such a transfer would fail at resolution. If you read my answer as a whole, I think it is clear on that point.

My apologies, that's what I get for answering questions late at night.
Sorry man, I'll check closer next time.

I know where you're comin' from--at this point, the rules forum keeps me from going crazy during all-nighters. 'sall good.