No.

1. Am I obligated to pay even if I never authorized the service orally or in writing?

-------You don't have to pay if you never authorized the service. I suggest you send a letter (registered mail) telling them that you never authorized the services and ask them stop from doing the same thing in the future.

2. Can I sue them to put fertilizer on my lawn without my consent and to come into my yard without my permission?

-------No, you cannot unless they damaged your property. You suffered no damage other than that your grass will grow better next year.