If you counter improved movement, does that also stop improved movement within powers?

No it does not.

What if you use the orange emotional spectrum that states a power/ability can't be used and use it against improved movement? Would that factor over to other powers and abilities that make use of parts of improved movement being prohibited from the power (but not shutting down the power completely)?

What i don't get when comparing the two is why can you prohibit the use of IM and where it is used within other powers/abilities such as Phasing/Teleport, Wing symbol, etc, using the emotional spectrum, but when you use a power like outwit to counter IM, it doesn't carry the same further effects on other powers/abilities?

Because you aren't countering all instances of Improved Movement, you are countering the specific instance granted by the character card.
It's not different from countering Charge on a character that has a Charge-granting hammer. The Charge found on the dial is countered, but the character can still use the Charge granted by the hammer.

Another good example is countering Carry on a character with and . It possesses Carry from , so that can be countered, but since also allows its use, then it can still use it.