The first thing to note is that this model is only rated to go down as low as 500 Khz with rated accuracy. This means that it is quite posssible that if you put a signal in that is too low in frequency then it will be attenuated too much and not be visible. So, if you try to put in a 5 KHz signal, you may not see the fundamental because it is attenuated too much.
If you are seeing a lot of lines at higher frequencies, you are seeing the natural harmonics of a rectangular wave. However, if you are putting in too much voltage, then you are probably also seeing the effects of distortion of the signal that is occurring inside the spectrum analyzer. We call this situation "over driving" the front end of the spectrum analyzer. You will be overdriving the analyzer with signals stronger than roughly -10 dBm, which translates to about 70 mV of signal. So, it would be wise to turn down the level of the function generator below this voltage and see if things simplify on the spectrum analyzer display.
Another thing to realize is that the frequency calibration of this spectrum analyzer is not terribly precise. So, you can't trust the display to show exactly a certain frequency, only about +/- 100 KHz unless you take additional steps. One useful thing is to recognize that the line that exists when there is no input is exactly DC and so you can use this to calibrate the x position of the trace on your display.