A few times a day, either the game gets stuck or the computer goes into safe mode and must be shut down. I'm afraid I'm doing damage. Has anyone else had this problem?

Those kinds of issues are typically caused by driver issues or hardware problems. Most games require specific graphics/display features that require properly functioning video drivers and hardware to perform. Safe mode is usually entered to allow you to diagnose and correct problems at a driver or hardware level.

What you should do is run hardware diagnostics and/or check out and update your drivers. These procedures also contain useful steps for determining if your graphics adapter is correctly set to run our games.