Luckily, Android's lock screen has deep dependencies (purges in-memory passwords for VPN, for example), so it can't be disabled be an app. That said, it can be prevented from appearing due to a timeout. Pressing the power button should always lock your phone.

Android already offers lock screen widgets, so it's possible FB Home will include something to that effect that would show even while the phone is locked.

It would be entirely optional to use that widget, however, unless FB Home is able to replace the lock screen itself. As far as I know, that can't be done without rooting the device.

No idea. I have been looking for some indication in the coverage but there's been none that I've seen. It seems clear (see my reply before) that it replaces the lock screen when it's not password protected.

Even if this isn't true, your friends with unlocked phones could be leaking your otherwise private posts to anyone who sees their phone.