Yes, reputation is a noun. For other questions about words just go to dictionary.com and type it in, if you misspell it a list will come up of similarly spelled words and you can select from there. :)
His reputation was sullied after the affair with the scullery maid.
yes.
A noun is a person, place, thing, or idea. A reputation is a thing, so it is a noun.
abstract noun.
While a noun is usually used to name a person, animal, place, or thing, it is also be used to name an abstract idea.