How to Mock a Service with Moq and Nunit in mvc application - prevent nulls

I was under the impression that mocking is faking data calls thus nothing is real. So when I trying to create my own Unit Test that are very similar to what other developers on my team are doing, I am thinking that this is not correct to be newing up the service.

    [Test]
    public void TemplateService_UpdateTemplate_ContentNameNotUnique_ServiceReturnsError()
    {
        Template Template = new Template()
        {
            TemplateId = 123,
        };

        // Arrange.
        TemplateUpdateRequest request = new TemplateUpdateRequest()
        {
            ExistingTemplate = Template
        };

        var templateRepo = new Mock<ITemplateRepository>();
        var uproduceRepo = new Mock<IUProduceRepository>();


            templateRepo.Setup(p => p.IsUniqueTemplateItemName(215, 456, "Content", It.IsAny<string>())).Returns(false);
            templateRepo.Setup(p => p.UpdateTemplate(request)).Returns(1);

            // Act.
            TemplateService svc = new TemplateService(templateRepo.Object, uproduceRepo.Object);

            TemplateResponse response = svc.UpdateTemplate(request);

            // Assert.
            Assert.IsNotNull(response);
            Assert.IsNotNull(response.data);
            Assert.IsNull(response.Error);

    }

So my issue is with this code:

TemplateService svc = new TemplateService(templateRepo.Object, uproduceRepo.Object);

Should the TemplateService really be newed up? What "if" the Service ended up hitting a database and/or file system? Then it becomes an integration test, and no longer a unit test, right?

TemplateResponse response = svc.UpdateTemplate(request);

Also, how do I really control whether this is truly going to pass or not? It is relying on a service call that I didn't write, so what if there is a bug, or encounters a problem, or return NULL, which is exactly what I do not want! ?