Yes, I've put a little sesame oil - not too much! in mine sometimes.
Ketchup - yes, it seems weird, but this is a fairly 'westernized' Japanese recipe, first developed by the Benihana guys when they opened the first hibachi style restaurants in the US. SO not a deeply 'traditional' style recipe. Japanese do love ketchup, tho, and mayo!
I've only used it with salads, but it would be great with cold noodles, or maybe some stir-fried green beans? Hamm, now you've got me going!