Furter, you can download the B&S Operator's Manual here:
http://bsintek.basco.com/BriggsDocumentDisplay/default.aspx?filename=flivAJX-nfBhU7y
This is the illustrated parts list:
http://bsintek.basco.com/BriggsDocumentDisplay/default.aspx?filename=Z6ntABVJ1DajI

Here is the illustration of what your carburetor should look like:

[Linked Image]
Your speed control cable is shown in your first photo at maximum speed setting. When the speed is set for maximum, as shown in that diagram, the governor spring should be moderately stretched, and it should move back to being free (no tension on it) at the idle setting. Your first photo shows the cold start position, which fully closes the choke as well as setting the speed for maximum. Your governor spring is somewhat damaged at the left hand end: it has been over-stretched, and should be replaced, though it will work after a fashion as it is.

To diagnose your issue with the way the engine runs we would need more information about what it is doing at the moment, that you don't like. If it is hunting (surging recurrently in speed, at about 2 second intervals) that is usually caused by lean mixture. It can be cured by turning the mixture screw anticlockwise a modest amount (probably a quarter turn). On the other hand if it is sluggish and/or blowing black smoke, you may be advancing the speed control too far, which closes the choke.

Can you post close-up pictures of the chain sprockets please? In the pictures you have posted they look as if they may be severely worn.