im assuming that you actually dont plan on carrying both pairs of shoes - rather, wear one and carry the other
pretty much any iata sized carry-on is sufficient to bring what you describe.
no iata sized luggage will have enough area to "hang" a suit. not even checked luggage.
not sure what you truly meant. but a coat will need to be folded atleast once around the belly (shoulder to shoulder width of 20" is enough for length of luggage). what problems exactly have you...