With your rates already being lower, I would not offer a lower rate. Think of it this way, if they were trying to negotiate a lower rate with another sitter who charges 20-25, I doubt they would get it lower than your $16. Just explain that you already offer a competitive rate.

Small dog breeds don't need as much exercise as bigger dogs. They tend to do well in apartments because you don't have to give them as much room to romp around. I would also suggest a non/low shedding dog like a poodle.

I have never had a bad experience using Craigslist and I have sold several things there. You should always use good judgement and be cautious when meeting strangers, whether it is someone from Craigslist or Rover. The way Rover suggests posting on Craigslist, it will only send them to your Rover page. They would still need to sign up with Rover to get access to book with you. No, there is no required background check.

Yes, I used the Sitter's Handbook and modified it to the questions I wanted to ask. Take a notebook with you to refer to the questions and write down answers.