I'm an English lawyer so my understanding of US legal terminology is not specialist. As I understand it, a lawsuit is a civil action e..g. for repayment of a debt, or a personal injury claim. It's possible that the word "cancel" is used by some US lawyers to describe the withdrawal of the suit - I don't know. I would choose "withdraw" in everyday English as this expresses what you are doing more clearly. In England, lawyers use the word "discontinue" but it's not common in everyday language. In England, "drop the charges" is the correct expression when the police / prosecutors decide not to pursue the prosecution e.g. if the evidence is not strong enough. It's possible that the police will ask your opinion as a victim in which case you might say "I'll drop the charges" or "I won't press charges". But technically, it's the police who decide on the charges.

1. You would probably say drop in both instances, not cancel. 2. Charge is usually used when you are talking about a criminal case, lawsuit for a civil case. 3. It can be singular (charge) or plural (charges), it doesn't have to be plural.