Unlike its successors, the tutorial campaign of RA2 sends you right into the Allied campaign after you beat it, and the second tutorial mission provides a rare Allies vs Allies scenario. Is it a good idea to start an Allied run from the tutorial missions?

The Allied campaign is available as a choice from the selection, and formally starts the actual campaign there, so it's best to start with that. Starting with the tutorial would be annoying for both the runner and the viewers.

Would it be a good idea to add a category that includes the tutorial missions and uses the hardest difficulty to serve as 100%?

That'd be a bit of a stretch. I do want to separate difficulties as categories, but there's some problems that come with it that I've mentioned before. The game doesn't provide anything more than difficulties for more things to do. The tutorial missions are pretty ignorable and wouldn't fit a 100% definition well.