Good Evening -
I'm sorry, but the question you have asked is extremely complex and it cannot be answered in this limited forum. I am happy to briefly explain why, and give you some very limited guidance on the issue.
(Q1) Is a catholic church that is closed and not in use no longer tax exempt.
(A1) The term 'catholic', without being capitalized, generally refers to a congregation of like minded individuals. For example, the term 'catholic' is not capitalized in the Nicene Crede.
Assuming that you intend to refer to Catholic, capitalized, the Catholic church itself is predominantly Roman rite, but the Holy Roman Empire is not limited to Roman rite churches.
If you are referring to what is commonly known as the Catholic Church in the United States, closing a church does not change its tax status.
(Q2) Please reference the tax law.
Here is a link to the 292 Tax Law decisions using the term 'Catholic': http://scholar.google.com/scholar?as_q=Catholic&n um=100&as_epq=&as_oq=&as_eq=&as_occt=any&as_sauthors=&as_publication=&as_ylo=&as_yhi=&as_sdt=3&as_sdtf=55%2C192&as_sdts=5&btnG=Search+Scholar&hl=en
(Q3) Furthermore is the catholic church tax exempt and its properties tax exempt.
(A3) If you are talking about the Roman Catholic Church, the answer is yes, it is tax exempt - but that tax exempt status is frequently challenged. The property tax status is not often challenged, because taxability of the property depends on taxability of the owner.