I think it would be feasible for most apps given that it's a million annual FIRST installs for free, but one would definitely need to find a way to monetize if the app gets too popular, which might be hard if your goal is to provide FOSS for the benefit of the community.
Why? FOSS apps can still charge money. Remember its free as in freedom not free as in free beer.
A lot more of them probably should as the alternative usually ends up in some company buying them out, such as what happened to mobile tools set of apps.
Yes it would, but afaik there's no mechanism in place that prevents your app from going over 1 million installs. So if it explodes overnight, you have a potentially large bill all of a sudden.