vMix is able to take "shortcut" commands remotely, this can be easily achieved through midi over ip or using the web controller (which I believe utilizes javascript). You would have to write a chat bot (twitch uses irc so there's plenty of info on how to do such, not personally sure about youtube though.), that would read chat commands and then sends either a midi command or a javascript command to activate a shortcut on vMix.

Definitely possible, but not really a default built in feature, so you'll have to do some work on your own to do this.

I'd agree. You could setup a cooldown with most chatbots for commands. The better option would be to do something like Znipe. Of course you're talking about a lot more setup, but would allow people to view the cams they want without changing it for the entire audience.