It would be fraud to make such a claim. Only the owner of the trademark can make such a claim.
Without a license, yes. Keep in mind the "Deep Note" is also a registered trademark.
Yes, trademarks are registered and are valuable properties to the companies that own them.
The purpose of a person doing a registered trademark search is if the person wants to register a trademark of their own. If their action is already trademarked, it cannot be trademarked by another person.
If I own a trademark and YOU use it, then our relationship is contractual and the terms will dictate when it may be terminated, if ever. Also, if I own a trademark then you have no right to register it unless you can prove you have an exclusive license from me to use it. However, if I licensed you to use MY trademark without reserving any rights to monitor the quality, then I may have forfeited any right to the trademark.
There are no registered trademarks for that phrase; common-law trademark may exist.
Yes. You do not have to have a trademark registered to use it. But if you are doing a large business or expect to expand trademarks are handled through the Trademark Electronic Application System (TEAS).
If you drive it on the street or park it on the street, yes. I has to be registered.
If it is your own or you have a license, yes. For example, something originally conceived as a decorative element may become part of a logo.
Yes, of course.
Phrases are not copyrightable. If a phrase is used on the packaging of a product or the advertising of a service it may be registered as a trademark or servicemark.
Short phrases such as names and book titles cannot be protected by copyright. They can be protected by trademark, but this is rare (Harry Potter, for example, is a registered trademark).
No. Because the illegal person either does not have a social security card of there own or they came to America Illegally.