Teams borrow from other teams all the time if they think it will provide an edge.
Look at the Pot of Gold. I want to say Kentucky or some other school started sending tons of mail to a recruit to try and lure them in. Not long after we started the Pot of Gold. As far as the building design it is similar to Michigan's Stadium, but I'm sure you could point to many stadiums that were similar during that period of history. We changed the location of the tunnel, so it certainly had some architectural differences, it's not like the design was an exact copy. As far as teaching them football, who cares? If it wasn't Michigan, some other school in the Midwest would have brought football to Notre Dame.
I think you're focusing too much on Michigan. Yes, we share some things with them, but we're Notre Dame, not Michigan. We have our own traditions, our own way of doing things. We've actually won some championships outright since the 40s, although sadly none since '88. You say we borrowed the Team# thing from Michigan, but how do you know other schools weren't doing it before them? I bet you Michigan probably stole it from another school first, just like some coach next season will be climbing trees and sleeping at recruits houses ala Harbaugh next year. Teams take whatever they can if they think it gives them some edge in recruiting.