Hi,
1 - From what I can tell, the Android team decided to mirror any and all status bar notifications to the lock screen.
I'm not aware of any "flag" when posting a notification -- to indicate that it should show in the status bar and not show on the lock screen.
2 - Android may collapse notifications, removing previews and buttons. Can happen to any app, as "decided" by system code.
To expand a collapsed notification, on 5.0, swipe it down (like scrolling, tap and move your finger down without letting go).
Attached screenshots:
- Gmail and AquaMail notifications, collapsed (initial state).
- Gmail and AquaMail notificatioins, expanded
Both show sender and subject for each of two new unread messages.