Is the following service layer correctly implemented with multiple repositories?
Business Model/Logic


These are two distinct things: your model and your logic should be implemented in separate  classes - the business model defines a Car class, and the business logic consumes it. In other words, I think your Car class is breaking SRP.

The way I see it (could be wrong) is pretty much like this (assuming MVC):



In other words, CarController only needs to know about a CarService, which gives it a model that contains everything the view needs to know - the CarService "puts the pieces together" so that the business logic "layer" can do its part.

I think having a dependency on IFileSystemService in your Car class makes that class be more than just a model.

Also, in "repository 2":

public Car GetPictureForCar(int carId)


I don't think it makes much sense to return a whole Car from a method called GetPictureForCar - I'd expect that method to return an Image.

This is even more surprising:

Car myCar = this.GetFileForCar(carId);


I'd expect GetFileForCar to return either a File class, or a string with the file's name.

Same here:

Image imgfile = _Repository.GetPhysicalFileLocation(carId);


A method that's called GetPhysicalFileLocation should be returning a string with the file's name. And to follow C# naming conventions, _Repository should be _repository (assuming it's a private field).