Does playing Vayne make you toxic, or do only toxic people play Vayne?

both

Neither, however the latter is closer.

Toxic people are drawn to champions with 1v5 potential (because they always believe they only lose due to crappy teammates and are never at fault themselves, so they want to play something that can carry crappy teammates [then they feed early and think they're not doing bad because their champion is weak early then blame the team for dying to the person they fed, hence why they're stuck in 'elo hell']), so more toxic people will gravitate toward Vayne than other champions. Same argument applies to stuff like Yasuo, Riven, Master Yi, etc...

However there are plenty of reasonable players who enjoy playing Vayne. You don't have to be toxic to be drawn to a champion - some people like a champion because of how they look, their lore, their 'personality' (largely the Voice over) etc...

Yes

Does playing yasuo make you feed, or does feeding make you play yasuo?

Vayne is edgy like Yasuo or Zed which attracts more kids to play them.

173, or at least that's how many licks it took when I was 7...