Yes, it is considered an extinct language. This simply means that nobody uses Latin as their native language. People can still learn, speak, write and read Latin, but it is not their primary language.
Yes, Latin cannot be spoken, thus it is considered a dead language. People that have taken Latin classes, however, are usually very good at vocabulary terms.
The definition of a dead language is a language that is no longer being used by people as their native language. In modern times, Latin is being learned and used around the world by many people, but it is not their native tongue. So yes, Latin is considered a dead language.