The preposition in question is "on", and its purpose is to show you where the dog chewed. You can remove the preposition to form the sentence "The brown dog chewed the rawhide bone." You can also rearrange it to find the preposition, "on the rawhide bone, the dog chewed" in what is commonly known as the Yoda technique.
A adjective phrase is a phrase the head of which is an adjective.
This is false: it has a very negative connotation.
It refers to a smile that is mocking or contemptuous (or a remark that is mocking or contemptuos) - so it's not a genuine smile, but an ironic and sarcastic smile. It has a negative and not a neutral connotation.
