A victim is a person who is hurt or injured, or suffer something unpleasant. A victim of burglary is a person who's belongings have been stolen. If you are on the receiving end of something, it means that you're being given something. But it's usually used in a negative sense. For example, you could be on the receiving end of criticism, bullying, or violence.
Profile refers to a person's physical shape or outline.
But we also use it to talk about a person's public image. Keeping a low profile means staying in the background trying not to attract attention. If a person is very well known, we say that he or she has a high profile. If you blow your top, it means that you lose your temper. In the US, firearms or guns are common type of weapon used in street crime.