Standalone thing is kind of solved. I realised that HISE itself won't run when I double click the binary (even though the execute permission is set). However it will run from the terminal or from the start menu (which is how I usually open it). So maybe this is a JUCE quirk or it's something strange with my system.
You don‘t. If you‘re exporting your project as audio plugin (Export as FX plugin), it will bypass all sound generators and process the audio input with the FX chain of the master container.