When I send an email requesting assistance from someone, I am tempted to close the email with the phrase “Much Appreciated”. Is it acceptable to use that phrase outside of a sentence?
I personally think that it is a matter of choice whether you would like to use it or not. I'd say "Much appreciated" is a casual sign-off that should be used for expressing gratitude for favors, like trying to confirm with someone to be a reference for your letter of recommendation or basically asking of someone to do a favor, like babysitting, housekeeping, etc. and once the favor is accepted the response would sign-off with a "thank you" to redeem any sense of expressed gratitude as genuine. It wouldn't be taken as condescending because you have not received any response that would anticipate a declined offer. Essentially if you are starting a conversation asking for a request, "Much appreciated" is the best sign-off. When in doubt, it's always best to use "thank you" in place of "much appreciated".
I don't understand how you can essentially say two contradictory things in that email and not notice it. "Requesting assistance from someone" assumes that the someone in question may, in fact, not comply for one reason or another; therefore, "much appreciated" is presumptuous because it assumes compliance. The only circumstance in which it seems appropriate to me to express your appreciation simultaneously with such a request is when the assistance has been guaranteed in advance because the someone you're asking has already said "Ask and ye shall receive".
ANSWER 1: No, unless there's no question about whether you'll get the assistance, and then it's not really a request for assistance but a request that the already requested or promised (or both) assistance be delivered now.
ANSWER 2: No, because terse expressions of gratitude are no expressions of gratitude except when asking a stranger what time it is. (Which is not to say that effusive expressions of gratitude are always appropriate either.)
ANSWER 3: No, because curt and peremptory expressions like Much appreciated are dismissive and condescending, IMHO.