Is my flash malfunctioning or am I just a dummy?

I got bigger flash that attaches to the top of my Nikon D5000, I was just experimenting so I didn't pay much. I was taking normal pictures just the camera's regular flash, but decided to attach the new one and test it out. The first photo I took turned out way too bright (as I figured) so I adjusted the shutter to be quicker, when I did this, this is what I got

When I adjusted the settings the other way, I got

I have no idea why my photo is being cut in half, and I would really appreciate it if someone more knowledgeable would enlighten this amateur.

One possibility is that your flash synchronisation is wrong. It fires too early or too late

You've selected a shutter speed faster than the cameras X speed. The X speed is the fastest shutter speed where all the sensor is exposed.

DSLR shutters work by having two curtains, the first curtain opens the sensor to light the second one closes it.

With speeds at or below the X speed, the first curtain has uncovered the sensor before the second curtain is released so all the sensor sees the flash. On faster speeds the second curtain is released before the first curtain has uncovered all the sensor, on very fast speed the two curtains only allow a 'slit' of light the duration of which is the fast shutter speed.

With flash photography there are two lighting components the Ambient (the light present before the flash) and the flash component (which is only, obviously, present during the flash).

Shutter speed does not effect the flash component as the flash duration is measured in 1/1000ths of a second. You use shutter speed to allow more or less Ambient into the shot.

It works like this

Shutter speed effects only the Ambient component.

Flash power effects only the flash component.

Aperture effects both as does ISO.

The X speed for a Nikon D5000 is 1/200th of a second.