First to your point 2. Any processes running in the background are still tied to your login, if you logout the processes are terminated. If you don't want the process to terminate on logout try:
Point 1 should be correct. Why you lost your screen session, I don't know. I use screen all the time without issue (admittedly I generally detach and log off when I am not using it) Is it possible a BOFH killed your screen session?