Attacks are single target by default, therefore the only way to interpret it that makes any sense is to carry the single across both terms. (Single target spells.)

I tested it with Katarina. Bouncing Blade/Sinister Steel does not give the bonus even if it only hit one unit, but Shunpo always did. So no, Graves' Buckshot will not trigger it.

Spells that have multiple coding scenarios such as Karthus' Q will proc as single target in the given situation.

It's the only one I can think of, but technically Morde's does as well, though it's an on-hit-effect and so irrelevant. Anyway, it's entirely possible I can't think of one, and just as possible that they'll come out with more in the future.

Does the effect proc on summoners spells like ignite or smite?