Three quick question about Flamethrower:

First question: The cost to play Flamethrower is "Exhaust equipped character". Now, in practice this is exactly the same as "Equipped character has 'Activate...'", but it doesn't actually say "Activate". So, if my Dr. Doom's wearing his power compressor, can my opponent use his Flamethrowers?

Second: Flamethrower says "Use this power only once per turn". I have out Mr. Fantastic and two other characters. The first character uses his Flamethrower, and Mr. Fantastic pays 2 endurance to transfer it to the second character. Can the second character use the Flamethrower? Essentially, is the "once per turn" limitation applied to the character or the equipment card?

Third: Flamethrower says "Whenever equipped character becomes stunned, KO that character". Again, Mr. Fantastic and two others are on the board. Character one has Flamethrower and becomes stunned. Mr. Fantastic responds by paying 2 endurance to transfer the Flamethrower to the second character. Is the first character KOed? Or, is there any spot on the chain to make the transfer which will prevent him from being KOed?

Thanks for any insight into these three questions!

Flamethrower is a payment power therefore PC does nothing.

Use Flamethrower once per turn. Once you use it, it is done for the turn.

There is no priority point for you to move the Flamethrower. Once both players pass on an empty chain, you move straight to combat resolution. You would have to move the Flamethrower before combat resolution meaning the character wouldn't have the +5 ATK when you did go to combat resolution.

To clarify a few points:Since activated powers are actually a subset of payment powers, the quoted reason isn't really accurate. The reason Power Compressor won't stop Flamethrower is simply that Flamethrower isn't an activated power, as its text lacks the word "Activate." (500.3a includes all this.)
Not quite true; in card design, a different wording or card template implies some difference in practice, as well. In this case, the difference can be seen in your second question---the difference being that it is Flamethrower's payment power, rather than the equipped character's. According to the Comp. Rules, restrictions on how often a power can be used apply only to the object which has that power; Flamethrower's text means that this once-per-turn restriction must apply to Flamethrower, rather than to any specific equipped character. (There is actually no equipment which gives the equipped character a once-per-turn power, so it's possible that it would be ruled to work as Flamethrower does. But the wording of the rules would make it much murkier than Flamethrower.)

As for the third question---like GDE said, if you want the benefit of the +5 ATK modifier, you can't transfer Flamethrower before the character stuns. And then when the character stuns, a triggered effect will be placed on the chain which, when it resolves, will KO the character. So there is a point of priority before the equipped character is KOed, but it won't really help you greatly, for two reasons. Firstly, the rules for transferring equipment state that you cannot transfer equipment from a stunned character, and so you can't move Flamethrower to another character unless you have a way to first recover the characer. Secondly, transferring the equipment, or even KOing it, wouldn't stop Flamethrower's effect from resolving and KOing the character which it had been equipped to.

Thanks guys! Very helpful. I'm relatively new to the game and these questions came up while I was playing my Gamma Doom deck against my friend's F4Fun deck. The once-per-turn rule on Flamethrower actually won me some games tonight!

Although the fact that Flamethrower isn't an activated power is extremely annoying to my deck.

Thanks again.