In general, we do not use étoile to translate star into French, apart maybe from Canadian French. As a native speaker from France, I would write it:

La star du rock a besoin d’un garde du corps pour la protéger des admirateurs fous.

Someone who would really like to avoid the anglicisme would use synonyms, like vedette.

However, it’s interesting to note that we do use the word étoile to translate rising star into étoile montante.

The second sentence looks perfectly fine to me.

The website that you’re checking probably uses very literal (word-to-word) translations. In general, a good practice is to double-check with other translation websites, some of them driven by communities such as WordReference.

Contrary to Reyedi, I don’t think that Je n’ai pas eu l’emploi en dépit d’être extrêmement qualifié sounds natural in French. I wouldn’t use en dépit de with an infinitive, I’d consider it as an anglicism.

To convey the same idea, you could say:

Je n’ai pas eu l’emploi alors que je suis extrêmement qualifié

or:

Je n’ai pas eu l’emploi et pourtant je suis extrêmement qualifié

Since I suspect the examples you’re giving are machine-translated, I wonder if admirateurs fous isn’t a translation of crazy fans, in which case, it’d possible to keep fan in French, but fan fous doesn’t work, whereas fans déchaînés or fans en folie would be ok.