I’d expect other civilizations to have also invented rockets, microwave ovens, radio communications, and more. Does another civilization arriving at the same thing as us mean it isn’t an invention?

Their observations of nature and their ability to predict stuff should be consistent with ours.

They might not use the same mathematical tools or the same physical models, but they should make the same predictions. That is, we might not be able to understand their theory of gravity, but whatever their theory is, it has to be able to make predictions about orbits, black holes, etc.

I don't think we could assume much about the mathematical concepts they use beyond that.

That's a pretty hard question to answer, and I think impossible to answer definitively (at least unless we met a civilization that did arrive at different concepts). It's kinda like the allegory of the cave; it's hard to envision another way of looking at the world, but that doesn't necessarily mean it's impossible for there to be one.

It’s a good question to think about.

A constant refrain of mine is that our brains have convinced us that they’re universal understanders, but we really don’t know that to be true.

Imagine the difficulty of dealing with aliens who have a different mapping of the physical universe, different than our mathematics, which is both true but literally and physically incomprehensible to us.

Their mathematics will most likely have fundamental differences from ours that have led them to solve problems we haven't noticed. They will be appalled at how we have missed such basic features of the universe. And we will be appalled at some things they haven't noticed.