I find it easier to tape the angles first but not all the way into the corner. I like that more because if you're pulling out of your angle with a flusher it's not going to hook the tape. But I know a lot of people putting all their three ways and then tape up to the beveled Edge. It's up to you to try and see which works better for you.
If I am planning to run paper tape in the three two-sided corners, should I let it run under that three-way corner piece, or just up to it?
I find it easier to tape the angles first but not all the way into the corner. I like that more because if you're pulling out of your angle with a flusher it's not going to hook the tape. But I know a lot of people putting all their three ways and then tape up to the beveled Edge. It's up to you to try and see which works better for you.