It's a nit, but it is interesting how many of the hand-picked examples on that page aren't right. Since they were hand-picked, presumably to show the product off.
Not necessarily. If you emit a batch of suggestions for 1 line and prune them with syntax checks you can already prune them and present them to the user while working on the next iterations.
The real difficulty is getting good checking on partial source code, some languages have better tooling for that than others.