I have never heard the word "manieth". Of course people invent new words all the time. But this one doesn't seem to serve much of a useful purpose. How would you use it in a sentence? Would such a sentence be more clear than one using more conventional words?
Like, it is common to ask a question like, "How many people came to your party?" How would the word "manieth" help? Like, "What was the manieth of the people who came to your party?" I don't see how that's any better.
In the case of your which-president question, sure, there is no commonly-used word or phrasing in English to turn that into a clear question. English-speakers stumble over that one all the time. Technically, the word "ordinal" meets the requirement, as in, "What is the ordinal number of Mr Obama's presidency?" But no one actually says that so you'd have to explain it, at which point you might as well find a different way to ask the question. I think most people would understand something like, "What number president is Mr obama?" Or you could say, "How many presidents were there before Mr Obama?" (I think many people would ask it as, "Which president is Mr Obama?", but that's very ambiguous. Someone might be inclined to answer "the one with the health-care plan" or "the one from Kenya" or whatever.)
I'd be happy to hear if someone else has a way to ask that question that is, (a) unambiguous, and (b) would be clear to most English-speaking people. i.e. a way to phrase it that uses words that most people would understand.