do they count towards your weekly chest?
i have heard yes, but i don't know if that means, for example, starting a non-depleted keystone and finishing it, but after the time limit.
or can you start a keystone that is already depleted and have that count towards your chest?

Yes. Depleted count for weekly box.

Any key you complete regardless of time spent in there will count.

This post was edited by iBruno on Oct 21 2016 10:42am