I can' believe this hasn't come up in our games before now, but if a character like Ms Marvel Skrull wants to be able to prob her attack role if she misses and wants to turn off her stealth, would that also turn off her hypersonic since they are both granted by the same single special power?

if she can, why?

She can choose which part of the power she wants to use. This only applies to powers that state that a character "can use X, Y, Z." This means that for any action they can choose whether or not they want to use any of those powers without having to cancel the entire power, and they can choose which of those powers they want to use on the next action. On the other hand, if a power states that the character "has X" then that cannot be turned off without canceling the entire power.

Note that the turning off must be done before the action begins, just like canceling.

Also note, that if you choose to not use the Stealth part of a SP (like Gambit or Ms. Marvel) that your opponent can also see your figure to use PC to make you re-roll.

Conversely, if you want to Outwit a special power that grants, say, Stealth, Hypersonic Speed, and Charge, then you have to counter the ENTIRE power, not just part of it, no? Or can you Outwit the specific ability?

Outwit counters the entire power. You do not get a choice of only countering part of it. For instance if you somehow managed to draw LOF to Skrull Ms Marvel with an outwitter then you could outwit "Exfiltration" but you could not choose only to counter her stealth that is granted by the power.

Thank you. You'd be surprised how often this issue comes up at my venues.

Can anyone link/refer to what part of the rulebook/faq/player's guide/eratta & clarification document where it explains this?

The way we had always ruled it at our venue, since it says 'can use X, Y, and Z' it was ruled that all powers are optional, meaning you don't have to cancel anything, and is assumed to be in use unless you say otherwise (which is how I believe the Batman TA worked as well...or at least here that's how it works).

it is located on Page 15 of the rule book

"A power is in effect when it appears on the character’s combat dial
through the stat slot. All powers are optional unless “non-optional” appears
in their description, and are not required to be used during your turn;
however, all powers (such as those activated by a specific type of action or
attack) are assumed to be in effect during an action unless you cancel it
at the beginning of that action. When a power is canceled, it is canceled
until the end of that turn and resumes effect at the beginning of the next
player’s turn."

So this means that all powers are in effect unless you cancel/not use(in the case of SP). Meaning that if SMM has her hyper/stealth SP and she runs then it means that stealth is on unless the player opted to not use it.

I also believe that is correct for Stealth, but think Batman's TA works a bit differently then Stealth and can be used or not at will. Basically can be turned on and off when you want. Not positive and too tired to look it up right now, but do believe it is treated a bit differently. If someone doesn't confirm yea or nay by tonight, I will try to look up the old rulings.

I'll chime in with my own question: can I disable a special power that gives me a particular symbol (i.e. giant symbol, wing symbol) by choice? Can I do it on my opponent's turn as well? For Example, Mordru's attack special power gives him the giant symbol.

Posts #2, #3 and #4 explain it nicely. There's also this entry in the Player Guide:
"When a special power indicates that a character “can use” a standard power in some way, the use of that standard power must be decided as an action is given and remains in use (or not in use) for the duration of that action including
any free actions that are granted by the given action."

You'd need to cancel the special power (since this kind of special power states that the character has said symbol, and not just can use it), which would remain canceled until the end of the current turn (in the case of Mordru, that would prevent him to use the other powers he can use thanks to said special power).
You can cancel it anytime an action is declared (be it Mordru's action or the one of another character), during your opponent's turn if necessary (just like any regular power).

Another related question/clarification...

"A power is in effect when it appears on the character’s combat dial
through the stat slot. All powers are optional unless “non-optional” appears
in their description, and are not required to be used during your turn;
however, all powers (such as those activated by a specific type of action or
attack) are assumed to be in effect during an action unless you cancel it
at the beginning of that action. When a power is canceled, it is canceled
until the end of that turn and resumes effect at the beginning of the next
player’s turn."

If a character has a special power that states it "can use" a power is that power also always on unless specifically turned off before a given action or is that power off unless stated otherwise?

Example #1. I didn't mention I was using stealth with Skrull Ms Marvel but I didn't say I was turning it off so because I am hindering terrain I now cannot use probability control on her missed attack roll.

Example #2. You didn't say you were using combat reflexes when I attacked your Nightwing so my Moloid clocked him.

There is no official ruling as Nbperp said.
But the way that he said he rules it is that it is on unless otherwise stated.
So in #1: you would not be able to prob due to not declaring it off.
in #2 they would get the +2 to def due to not declaring the power off.