Honda City went for service and came back with a windshield crack

Bear with me, I am absolutely new to driving and owning a car. It's been 3 months only. I gave my car for servicing 2 days ago at Arya Honda Sweri and when the car came I see this crack on the windshield. I sent the car back and they accepted it's their cleaning departments mistake. Now I have few questions. 1.) They said they will change the windshield and I don't have to bear any cost. They said the glass is unavailable at the moment and will be available by Thursday and the new windshield fitting will be done by Friday. Hope this is true and nothing is a lie. I have asked them for an email confirmation and I have written an complaint too. 2.) Should i be worried as my car is in the service center and if they will fiddle with car parts? 3.) If I get my car back and ask them to take the car on Thursday and fix it. Will they overlook it or keep postponing it? Worried here? 4.) They know I am a woman and i have zero knowledge on this and i have no male support on this matter. 5.) I have not paid the servicing money because this was the issue. And now I am worried what if I clear the bill and take the car, then they won't look into this matter? Please help on how I should proceed.