How can I convince my department that I have the academic freedom to select textbooks and use multiple-choice tests in my courses?

As a current undergraduate student who recently attended a Community College I personally agree with at least requiring all professors to use the same textbook. It means that students from different sections are able to study together more easily than if the books and overall approach to course are different as I'm seeing in some courses at my current University. At least some Community Colleges allow you to change courses up to at least one week into the course with no extra fees, which means that if you find a professor doesn't suit your learning style you can change to another professor, but if you need to buy another text book that would become significantly more difficult for those students. This is especially important in a multi-course series like Calculus where its possible that you could purchase the textbook for the entire series for a fraction of the cost of purchasing the book for each course individually.

I know I'm probably in the minority regarding Ebooks as a large number of my fellow students in the time I spent at a Community College preferred them, but I always preferred a physical book as most Ebooks come with a subscription of some kind which requires renewal every semester for a significant portion of the cost of the book.

And as a final point regarding selection of teaching material, it seems that your department only requires you to use the textbook they decide is best and you are able to supplement your teaching materials with animations and MatLab objects as you see fit. This was a very successful scheme for my Calculus 3 professor as they were able to quickly show us what the concepts looked like as 3D objects in a way they would have been unable to on a blackboard.

It is my understanding that as a tenured instructor, I am able to teach the class in the pedagogical manner I believe is best for my class. Wouldn't this include what textbook I use and the types of assessments I use?

At least one of your questions is discussed on the American Association of University Professors’ website:

I have been asked to teach several sections of an introductory course, but I do not want to use the textbook used by faculty colleagues in the other sections. I believe it is poorly written and replete with errors. Do I have the right to assign a different textbook?

In a course for which you are the only instructor, you have the right, under principles of academic freedom, to determine the texts (and other materials) the students will be required to read. Your right in this regard is not absolute, however. The texts should be related to the subject of the course and practical concerns about availability and cost should be considered. Still, the principle is clear that the faculty member who is solely responsible for the course has the freedom to select readings for it.

Regarding assessments, I don’t have an authoritative source, but I suspect you are correct that it’s up to you to decide on your methods of assessment, assuming they are within the norm of what’s broadly considered acceptable in higher education. This AAUP web page has additional resources where you might be able to find some relevant guidance.

It is my understanding that as a tenured instructor, I am able to teach the class in the pedagogical manner I believe is best for my class.

In principle, I agree with this, and I believe that you should be able to run the course based on your considered professional opinion of what is best. But keep in mind that this is a two-edged sword! As I see it, academic freedom isn't unlimited license to do what you want; it's the freedom to try what you want, and be judged based on the results. (The same applies to academic freedom in research: nobody will stop you from working on the problems you find interesting today, but in the long run, they had better lead to publications.)

I don't know what the tenure system is like at your institution, but commonly there is some form of ongoing evaluation of a professor's effectiveness in teaching, with potential consequences if it is poor. And if you're pursuing these methods against the advice of your colleagues, some of your peers may be looking for evidence that it's not working (or may see your choice as ipso facto evidence of poor teaching).

So if you go this route, it would be wise to try to measure to what extent it is successful, in some way that your colleagues will find convincing: exam scores, evaluations, grades in this and subsequent courses, common assessments, etc. If it goes well, you'll be able to show that your methods are effective. And if it doesn't, you'll know that you need to change course quickly (and your responsiveness to evidence can itself be a point in your favor).