Hi OP. It's a horrible time after hearing the diagnosis and that things will only progress, not resolve.
You might feel like diving in and doing ALL of the research about everything from the medical issue at hand to logisitcs of settling an estate.
First, allow yourself some space to just sit with this news. Then I would make a list of things you want to follow up on. Allow yourself times to address this list, but there should be times to be "unproductive" giving yourself a break from it all, or just connecting with other family members.
Keep up with the basics, food, sleep, walks, sunlight. If you think you need a grief counselor or a therapist that would be a good thing to start.