Just wanted to add my input, although a little late. Many auto-focus issues can be resolved if we understand how our focusing system works. The KP has 27 AF points, 25 of which are cross type. I'm guessing because you are familiar with film cameras, you've used a split-prism focusing screen.
AF systems work in a similar way. They line up edges until the subject is in focus. Having a cross type AF point allows the camera to use horizontal AND vertical lines. Knowing this, I can choose an appropriate AF point and place it on an edge, never on the center of a solid-colored object. This allows the focus system to quickly and accurately obtain focus.