Back in the ‘80s I wrote many, many freelance articles for music magazines, some of them involving interviews with musicians. Here’s my off-the-cuff answer to your questions:
As a general proposition, I would not expect a publication or website to tell you “we will keep you in mind for celebrity interviews we might want” unless you already have a strong, ongoing relationship with the editor who assigns such interviews.
Many celebrities make themselves available for interviews only to promote their current projects, and only to media outlets with a fairly large audience. These sorts of opportunities tend to be time-sensitive.
To get started, I recommend you pinpoint one or two publications/websites and figure out a story idea to pitch to an editor, the story to involve a celebrity who’s got an upcoming or new project to promote, and whose project and/or career activities are somehow relevant to the publication or website. If you have a prior interest in the celebrity or the subject matter, so much the better.
Example: You contact your hometown newspaper’s features editor because a well-known athlete who grew up in your town has a bit part in an action movie that will be hitting theaters in a few months. You pitch the idea of interviewing that athlete about the film. Before making that pitch, do some background research on the athlete and the film, so that you can discuss them intelligently.
If you make a few well thought-out pitches that have some relevance to the publication or website, you might get the go-ahead to try contacting the publicity team for one of the celebs. Even if you don’t initially get an assignment, an editor may decide he or she likes your energy and enthusiasm, and will perhaps give you a try-out assignment doing a project you did not pitch. If offered this opportunity, take it.
Best of luck!