Google Scholar will show you what works by a particular author have been cited, and how many times, IN publications that are visible to Google Scholar. There are a number of problems with the way citations are searched and cited, according to Peter Jasco (2008), among others. Not everything is visible or searchable by Google, it sometimes treats other elements as names, and GS does not do well in distinguishing authors of the same name if the name is common. Also, it may find your name as an author on a journal's site, versus someone having cited your work there in an article or book.
Google Scholar stacks results by how often particular pieces have been cited by others, and how often pages are connected to or linked to by others, as well as by other factors.
Some other databases, including Web of Science, APA PsycINFO, Ebsco Business Source, Communication and Mass Media Complete, and others will allow cited author searches for the journals and conference proceedings that they cover.
Authors' names can vary in the way that they are recorded and cited. Google Scholar prefers the author's first initial and then last name, but I find it more effective to search for a particular author by putting the author's initials and last name in quotation marks: "Laurie Rene Lawrence" or "LR Lawrence", or with the name reversed, such as "Lawrence, Laurie Rene" or "Lawrence LR"
This will find 1) works by an author with that name and 2) works citing an author with that name.
Be careful. Last names and initials in common can still cause confusion. Even a less common name will usually draw up more than one author's works.
You may search for who has cited a particular work by searching by a cited author's name. Also, you may use the title of a book, a composition, a film, a work of art, or other intellectual product to find out who has cited the work. For example: "Fight Club" as a search shows citations to the movie and to the book that the movie was based on, and to the works of people writing about either one.
Google Scholar finds both journal title abbreviations and the full title of journals, but it's not consistent because what they are finding is not content that has been purposely created to be searchable. For specific cited references, you may search using an author's name AND a journal title, but not just a journal title, as that isn't distinctive enough. Choices on the advanced search screen can streamline this type of search.
If you want to find out if someone has a profile page in Google Scholar, you'll need to login to Google. Then go to the Google Scholar home page. In the upper left corner, there will be a group of small horizontal lines, sometimes known as a hamburger. If you click on that, one of the choices in the dropdown menu is Profiles. Search for your person in that portion. Searching someone's name in regular Scholar will usually just get you their publications or other projects.