An update...
This post relates to both the post directly above and my post entitled "Auto-Complete" from a few days ago, which Paul responded to. I just discovered that auto-complete does work, in a sense, because if I continue to type the name I want until it is the only one left in the drop-down box and then hit Tab, even without hitting my arrow keys, the program will enter that name into the field and go the the next field. This also address in a way my question about Method taking me back to the first field on the screen. I've found that if I follow the procedure I just mentioned, and hit Tab without first using my arrow keys, it will move directly to the next field, and not back to the first field on the screen. That still doesn't answer the question of why using the arrow keys causes Tab to send me backward instead of forward, but it does solve my immediate pain point. Hope this helps.