Hello hanz,

When it comes to Macro photography, it's very normal to use Manual Focus instead of AF. With AF at such close distances, it is very difficult to focus exactly on the point that you want, which you have already discovered. It'll be hit and miss. Switch to Manual, or better, DMF mode, and from there, adjust it.

Menu > Camera > AF/MF Select > DMF or MF

With DMF selected, the camera will attempt to AF first; when it has focus confirmation, you can then turn the focus ring to adjust your focus, while still holding half-shutter. Once you have decided on your focus, full depress the shutter.

On your issues with the small and thin depth of field (only center is in focus, rest blurry), this is a common factor in macrography. The closer you are to the subject, the less depth of field there is, hence creating the slice of sharpness across the center. To overcome this, you will need to use a larger Aperture setting. I presume you have shot all of this pictures with the Aperture wide open (3.5). Try going beyond F8, till F13 to get better results. The larger the aperture number, the more depth of field you will get.

To easily control the Aperture, switch to Aperture Priority Mode. With this mode, you can manually adjust the Aperture size, while the camera determines the Shutter Speed.

Menu > Mode > Aperture Priority

Do note, that with a larger Aperture, you will need more available light. If there is not enough light, the camera will compensate by increasing the ISO or slowing the Shutter Speed, hence making it harder to hand-hold and shoot your objects. I recommend a Tripod, to keep your camera still while the camera dials in a long, slow shutter speed. The flash will not help here, as being this close to your subject, the lens itself will obscure the path of light from the flash.

So in short:
More Depth of Field = Larger Aperture = Higher ISO / Slower Shutter Speed

Another thing to keep in mind: The NEX prefers to up ISO levels first before increasing anything else. If your ISO is set to Auto, more likely than not that the camera will increase it all the way to 3200, before actually decreasing shutter speed.

Hope I helped.