I believe the thesis in this is actually the first sentence considering the rest of the story talks about that first sentence.
Answer:
The butterfly net
Explanation:
The noun or noun phrase that's modified by the prepositional phrase is: The butterfly net because the prepositional phrase is modifying (describing) the net, not Kristy
The conflict is pretty much the main subject
Explanation:
The actual work of tattooing it on your skin would probably qualify like that but they also often do the design work on the tattoo itself (they would own the copyright to that). And if they don't do it then they adapt work from somebody else (who owns the copyright to the image).