Can you identify an isotope using density, radioactivity, or both?

Answer 1

Both.

Each isotope has a very specific radioactive signature (most are well documented). There are spectrum analyzers available that can identify isotopes immediately using the radioactive signatures.

Each isotope has a specific atomic weight, but with the same chemical properties as the 'stable' element, so it may be weighed (and density differentials determined). This is how U235 is refined out of a mix of U238 and U235, with centrifuges (using the mass differential).