Unless you are single and don't care if she calls you, don't give your home number. Use a prepaid cellphone. Work number is different. Yes providers will call the work number to see if you work there. By choosing a well respected/reviewed provider you are well assured of discretion in her phone call. Most likely you will never even know she called. Many use different reasons such as salespeople or something.
b-
Maybe I missed this on another post, but what does the potential provider do when you submit your work and home numbers on their online form? Are they just checking that it's a real number that matches your other submitted info or are they going to call and talk to someone and ask questions.
Unless you are single and don't care if she calls you, don't give your home number. Use a prepaid cellphone. Work number is different. Yes providers will call the work number to see if you work there. By choosing a well respected/reviewed provider you are well assured of discretion in her phone call. Most likely you will never even know she called. Many use different reasons such as salespeople or something.
b-