Is it an infringement to search for a cartoon of a [cat] from Baidu as its own business logo (for various occasions)?

Hello. The answers for you are as follows:

1, commercial use is infringement without the author's consent. It is also illegal to publish other people's works on the website of commercial material library without authorization.

2. If it is used after being modified in another person's work, the consent of the copyright owner must be obtained. Without consent, it is also infringement.