It's because the operative term would be "もう一枚" (one more/another), 一枚 comes with もうand not マント. You can rephrase it into マントをもう一枚出だして and it would mean the same.
Note that you could also say "もう一枚のマント", but that would mean "the other cape".
See def 5.
This が is a plain subject marker, and it's not interchangeable with の. This 〇が1人 is a contracted version of 〇が1人いる. いる has been omitted because it's redundant when counting things.
In English, you count sheep like "One sheep, two sheep" (but not "There is one sheep, there are two sheep", which is too cumbersome). In Japanese, we say "...