Best video performance with the Nikon 5100?
The focus issue is a side effect of contrast based autofocus.  The camera basically is guessing at what "in focus" means by analyzing the lines in the image and if the overall sharpness is better or worse than it was at the previous focus setting.  This process ends up meaning it will move through the focal point and out of focus again as many as a few times before settling on the best point.  Using manual focus with a narrow aperture to increase depth of field is generally your best bet to get a suitable result, but may require fairly bright lighting.

As for microphones, the best mic to use is going to depend on what kind of look you want.  If you want a handheld mic, the Shure SM58 is a relatively cheap and standard mic.  You can also go with a shotgun mic if you'd prefer something off camera that can pick up clear audio, though it might be harder to use properly without an operator pointing it if you move much in the scene.  The in-between option is a lapel mic which can be worn and remain fairly inconspicuous.  This is the most common approach when a boom operator isn't available and you don't want to be visibly holding a microphone.

There are a wide selection of shotgun and lapel mics available.  Your best bet will probably be to jump on someplace like B&amp;H and start looking for well reviewed mics in your price range.  If you have any more specific questions about what type of mic to choose, we could answer general questions about what features would be best to look for if you have particular concerns or needs.