I seem to get very confused about what to do with the diaphram generally when singing? I get you're meant to breathe in so your diaphram/stomach expands rather than lifting your shoulders but once you are singing (particularly for the high notes) are meant to push gently/strongly to hold it out expanded fully for 'support', let it collapse naturally after it's been expanded fully on the breath in or pull it in to reach high notes? Or is it different for different things?  

In general, we want to gently engage those low belly muscles down and out while we sing. Pulling up and in won't help (in my experience), and letting it collapse will also diminish your support. Relax on the inhale, engage on the exhale. Here's a full lesson on breath support that may answer more related questions: https://www.youtube.com/watch?v=VzLV8rVyIBo.