Reasonably short quotes, properly cited, should be defensible under fair use.
No, quotes are not automatically in the public domain. They are typically protected by copyright law, unless they are very old or the author has explicitly placed them in the public domain.
To copyright quotes, you can include them in a larger work that you register for copyright protection. This will protect the quotes as part of the overall work. Additionally, you can also register individual quotes with the U.S. Copyright Office, but keep in mind that the quote must be original and meet the requirements for copyright protection.
No. You could copyright a drawing or photograph of the logo but the logo itself would have to be protected as a trademark.
Individual words are not protected by copyright.
Yes.
Once a work of sufficient originality is fixed in a tangible medium, it is automatically protected by copyright.
Yes. All of the photos taken in the movie are protected by copyright.
Short phrases cannot be protected by copyright, but there are several registered trademarks for that phrase.
Yes; architectural works are protected.
The 1952 movie is protected by copyright, and will likely be protected through 2047.
The physical tape is not protected by copyright; the content on it probably is. Commercially produced tapes are certainly protected.
People cannot be protected by copyright.