Regarding Singed build: I usually build something along this order (lets just assume against heavy AD team): Tear of the godess -> custom boots -> Rod of ages -> Seraph's embrace -> Rylai's -> Frozen heart -> custom item.
I was thinking about building Liandry's torment. Anyone who has experience with that item on Singed? I could imagine it would fit perfectly together with a Rylai's. I was also thinking about rushing rod of ages. I guess it kind of depends on the circustances.