With my face blindness, I need to see a person enough times to be able to recognise them out of context. (That could take about a month or two on a daily basis.)
In the case of celebrities, I came to know Robert Downey Jr. as Iron Man and Hugh Jackman as Wolverine, and I could not recognise them when they were acting in other movies. (Now I think I can recognise Robert Downey Jr outside of Marvel movies, but I still can't recognise Hugh Jackman because I've not seen his face enough.)
Similar to NickRowler's case, there are instances where I just can't tell two people apart in a group (both for movies/shows and in real life), and it'll take me a month or two to be able to finally tell them apart. This also happens with comics/anime and it's a bit of an inconvenience.
As for making avatars of people, of course I'm going to need a reference if it's someone I'm not familiar with, but if it's someone whose face I can picture with my eyes closed, then I should be able to create an avatar of them.