Yes; logos and slogans are also protected by trademark law.
Ideas cannot be protected by copyright. If your idea is a new process, you may wish to seek patent protection for it.
Civil defense posters that are entirely works of the U.S. Government are not protected by copyright.
Such a name, if protected, would be protected as a trademark rather than a copyright. If there is any chance at all that anyone would guess for one second that the person named is endorsing the product being advertised, you would absolutely need permission.
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.
Yes. All of the photos taken in the movie are protected by copyright.
Once a work of sufficient originality is fixed in a tangible medium, it is automatically 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 models are not eligible for copyright protection. The packaging artwork, advertising (excepting slogans), and descriptions are all copyrightable (provided they meet the necessary criteria). The character models themselves could be, and probably are, protected as registered trademarks.