I guess its probably because you are using long exposure to take these shots, and the person moved (even a little) so he/she will turn out blur. Try using slow sync flash. Basically what it does is, to capture the background using long exposure while illuminating the person with the flash. With slow sync flash, the shutter will still stay open after the flash is fired until the set shutter speed is up. The person will still need to stay as still as possible during that time.
Right. It is primarily caused by slow shutter speed. Flash _might_ help.
As for focussing problems, most consumer digital cameras focus by means of contrast detection, which means it will focus on anything which has more contrast - in this case, the background. You can try to alleviate the problem either by lighting up the subject (using torch or AF-assist of your camera/flash if it has one) or by a combination of manual focus and distance gauging.
if you are relying purely on the ambient lighting to capture the person, it's likely that he/she will be blurred. It's easier to use the flash to freeze the person and a wider depth of view (small aperture) to ensure that everything is in focus. Tat's just my view...