You don't need to prime, but the nail holes might flash if you don't double coat them. You can use a primer for this or you can use the low lustre topcoat.

The L shape baseboard is a good solution for the situation. Shame on that installer threatening to just leave. That's wrong. Next time someone in your house threatens to leave, let them & find someone else. Pay installments. Do not pay someone fully until it's done fully. A good Pro respects his clients wants. If the client wants something different sure no problem. More work = more pay. A change will cost more, but if client wants it, a Pro will happily find a solution & appreciate more work with more pay. I would not hire that person ever again. Thankfully, it wasn't a big job & it all worked out. Nice door, btw.

I hate full casing, "Craftsman" or not. Looks and is cheap.

You have a very beautiful and big house. I really like it. It seems to me that the new garage doors should be beige. This color will be ideally combined with both white windows and brick facade color. I recently also ordered the installation of new garage doors of the easyfixnashville.com company. The guys are professionals; they even helped me find the perfect gate for my garage. It was high time to do this because my old garage doors were not automated, and it was very difficult for me because of this. In winter, it is especially difficult when it is cold to open and close the garage doors manually.