1) Go into Yast - System - runlevel editor; make sure that runlevel 5 is selected as the default. If it is, then go into the edit screen (runlevel properties) and check to see what services are starting at runlevel 5. Make sure that xdm is checked "yes" for runlevel 5. If not, select it and choose the reset service option, then reboot.
2) For your GUI problems, run SaX2 (either from your GUI desktop or from the command line) and edit your display settings. Make sure your screen resolution and frequency are set correctly; having the wrong frequency set can cause the kind of behavior you mentioned.