Check Screen Session – How to Verify If in Screen Session

Try using the -t option to ssh

ssh -t root@my.machine screen "tail -f /var/log/messages"

From man ssh

-t      Force pseudo-tty allocation.  This can be used to execute arbi-
        trary screen-based programs on a remote machine, which can be
        very useful, e.g., when implementing menu services.  Multiple -t
        options force tty allocation, even if ssh has no local tty.

You can change the default keystrokes in screen, but you will encounter the same kind of problems, just with other keystrokes. Byobu makes it easier to setup the basic keystrokes for screen. In byobu, the cycling back in session log with the mouse wheel is activated, too, so you could either use it or see how it's set in /usr/share/byobu/profiles/common.