The definition of "fake news" is a list of 21 conservative web sites chosen by BuzzFeed. For some reason, BuzzFeed wasn't in that list.
Unsurprisingly, by that definition, fake news is primarily spread by conservatives! Chart C shows that as the strongest result by far. Chart B, going by age, is a weaker result. Well yes, it seems that conservatives live longer (living less dangerously?) or that people turn conservative as they age. It is well-known that older people lean conservative.
This study is, itself, impressively fake, just like BuzzFeed.