Is it possible to have SonarLint for IntelliJ IDEA enforce only the rules I have enabled on my Sonar server?
SonarLint 1.0 for Eclipse and IntelliJ do not allow to edit the quality profile (or set of rules) to be used for the analysis. Moreover, SonarLint 1.x works completely independently of a SonarQube server (having a SonarQube server is not a requirement), and therefore does not have the ability to reuse a quality profile defined there.
SonarLint 2.0 will have an optional mode that connects to a SonarQube server, and will offer this feature - but this isn't available yet.