Would myeloma-related proteins or an m spike show up in routine blood tests - or specialized tests only? What about protein in routine urine test?

Yes/no/maybe. A routine chemistry may show an elevation in the total protein or globulin levels plus or minus high calcium or kidney dysfunction but the ultimate diagnosis is made with an SPEP + IFE. Urine electrophoresis may also show the protein if it's small enough to filter through. That is not always the case, though.