So for HFE, the gritty work of setting up the Velocity context is done here. Might not be the cleanest documentation, but at least it should show you what’s available. As you can see, the Velocity user variable refers to the actually authenticated User object, which has all the fields listed here.
To tell if a User has a particular role it’s best to use the User#hasRole() function as this handles certain logic like nested roles and the idea that the super has all roles. To do this from Velocity, you just need:
<excludeIf velocityTest="$user.hasRole('Admin')">
<!-- content goes here -->
</excludeIf>