Sure you could. I'm not, I don't think its in the spirit of local first. And I wouldn't pay money for that, but if you or someone else wants to build that kind of software - its a free world :)
It’s easy to say you wouldn’t do that, but if it gets to the point where you have an employee helping you out and in a downturn you have to choose between laying them off or pushing an ad to keep paying them one more quarter, you might reconsider.
IMHO, a fully local app is an app that can run locally with all the functionality, not that it's isolated from everything else.
Browser, email client (running locally on your device such as Mail.app, mutt, Outlook,...), Zed (text editor, runs locally but can check for updates... as can many other modern apps)...
i could be wrong but I think they're referring to the winrar model, where there are occasional "annoyances" that you can either ignore or pay to get rid of.
Yes, you are. You can find tons of purely local apps that monetize themselves with ads.