Count it as a blessing that your dad didn’t conduct his life online. You might not know what bills need to be paid or what accounts he had, and you would be drowning in a sea of usernames and passwords. It’s much easier if he dealt with life by mail. You will get his bills, and you will pay them. If they are bills for services that are no longer needed, you can contact the company and see what you need to do to get the account cancelled. You will also get statements from his bank accounts, credit cards, etc. Eventually, you will need to do something about these, but not in the next 5 minutes. (Look at the bank statements, though, for anything that’s being automatically deposited or withdrawn every month. Some of these things may need prompt attention.)
You need a lawyer. If not the one who set up the trust, you need another one who practices in the community where your father lived. You also need a funeral director. These people are valuable not only for the services that they themselves provide but also because they can refer you to other services that you need.
I would contact a Realtor sooner rather than later. They have incredible connections in their community and can find you almost anything you might need (including contractors who can clean snow off the sidewalks or mow the lawn). They can also tell you if there’s anything that needs to be done to the house to make it more saleable (maybe some painting? replacing broken appliances?), and you can get started on that right away.
It sounds like your father lived alone. So did mine. Two of the most important things my sister and I did after his death were to clean out the refrigerator and take out the trash. If these things are neglected too long, it can get icky.
Did your father have a car? You will need the title in order to sell it, and you may need to sell it promptly. (After my father died, we could not find the title, and it took much effort to get a replacement. In the meantime, we got an offer on his house very rapidly, and that means that the car was a problem. If we sold the house, we couldn’t leave it in the driveway, right?)
Don’t worry too much about the number of death certificates. Get plenty, but if you run out, you can get more.
Keep track of every expense you incur when working on the estate, and make sure that the estate reimburses you. You may find yourself spending a bundle. In my case, when I served as executor for my parents’ estates, I was able to be reimbursed for funeral expenses, bills I had paid, travel expenses, etc. long before the estates were settled. But you’re dealing with a trust, so the situation may be different.