Kate should not be shipped with anyone (except possibly her braid).

Snape should be shipped with Lily, or at least he really wanted to be. None of the other Snape ships make much sense to me. In fact, I don't get all the Snape love in fandom, but I suspect Allan Rickman has something to do with all that.

It's sort of like how nobody in RH would have paid any attention to Guy of Gisborne if Richard Armitage wasn't Teh Hawt! ;)