This isn't Yu-Gi-Oh!. The effect doesn't necessarily have to do anything when you put it on the chain. In the case of Mystical Paralysis (or any effect), you need to look at the targeting requirements and timing requirements (effects that say this attack or similar). Mystical Paralysis has a targeting requirement of 'target character'. It does not say 'target ready character'.
There is also a difference between paying a cost and performing an effect. To pay a cost, you must perform the action. Mystical Paralysis has a cost of exhausting your Dr. Doom. If Dr. Doom is already exhausted, you cannot pay the cost, so you cannot put Mystical Paralysis on the chain. Exhausting is defined as giving the exhausted characteristic to a character. If a character is already exhausted, you can't give that characteristic, because it already has it.
As part of the effect, however, the effect just will do as much as it possibly can. In the case of Mystical Paralysis, it will attempt to exhaust the character. If the character is already exhausted, then Mystical Paralysis will do nothing, but it will still try. Similarly, with the Mephisto 8 drop, if you have 2 characters on the field (one being Mephisto, of course), when the time comes for the effect to trigger and resolve, you will need to KO your 2 characters. Even though it says to KO 3, you must do as much as you possibly can to fulfill the effect. You KO'd 2, which is as close as you can get to 3. Even though you can't KO 3, you still need to try.
Again, though, it is a distinction between costs and effects. If you need to pay a cost, then you need to do what is required (exhaust a character, stun a character, etc.). If you are just trying to fulfill a portion of the effect, you must do as much as you can, but if you can't, well, too bad.
This is why, incidentally, you can redirect a stun from Tim Drake to a powered up Red Star. You still TRY to stun Red Star, but he can't be stunned, so the effect essentially does nothing.
In .VS, it doesn't matter if an effect won't seem to do anything when you put it on the chain. All that matters is that costs are paid, targets are legal, and timing is correct. As long as that is true, it doesn't matter that it won't do anything.