Poor fish. It's perfectly normal for imports to bite their fins, particularly if it took six days for the parcel to reach your house.
The lethargy and difficulty swimming was probably down to stress from not only new water conditions, but also the trip from your transhipper's place to yours.
There are very few diseases you can catch from pet fish. The only one that immediately springs to mind is fish TB and that's only if you have open wounds that come into contact with infected fish/water.
I too hope the fish were dead before you flushed them as that is a horrific way to die.