What do US universities mean when they mention anything above the "Calculus" course?
I think your question is:  What does calculus mean?
Calculus would usually include learning to compute derivatives and integrals.
If you are learning to prove the theorems used to compute derivatives and integrals, that would be more advanced than calculus.

linear algebra analysis 1, multivariable analysis, topology, group theory

All of those would usually be considered more advanced than calculus.