I was in grad school (albeit a different type of program than Jane -- PhD in psychology at a large state university), so just chiming in. Take this with the bias/understanding that I can only speak to the experiences I know of as someone who went through a PhD (not MFA or MA) program at the university that I attended (and also the experiences I know of through friends in other PhD programs at the universities they attended, which were largely identical).
(1) Not at all weird to teach the entire class. I taught "Intro to [specific Psychology Subfield]" for several years as a "TA." I taught 2 sections of 50 students each, entirely on my own. Well. There were 12 sections and 6 of us who worked as TAs, teaching 2 sections of the class each (not discussion sections or labs, mind you -- sections meaning different time slots for the class, which was a typical Intro Course Powerpoint Slide Lots of Info Survey Course sorta deal). There was a "course supervisor" who was a PhD holding professor, but that person had 0 to do with the class. All she did was decide what textbook would be used and be the person who would act as the "higher up" PhD authority figure should something ever need to escalate to the level where she would need to be involved (e.g., yes, a plagiarism accusation...I wouldn't technically have to check with her before accusing a student of plagiarism, but I would likely notify her before speaking to the student just to make sure she felt comfortable with what I was saying, to shield myself from liability or consequences if something went wrong, basically). 99.9% of my students never met her or even knew what her name was. My name showed up on the course list when they went to register for the class, and my name was the only one they ever saw during the course of the semester. I designed the lectures, taught them, designed the quizzes, administered them, graded them, and assigned final grades, entirely on my own with no consultation with anyone else. This was what I was supposed to do, and this was very, very common -- more common than not. Which brings me to...
(2) Not at all weird to start doing this pretty early on...even as early as your first semester. (It's the #1 way that grad students get funding, so yeah, you usually do have to start pretty much right away). Your first couple years you might be a grading TA, where you do nothing except grade papers/tests, if you get lucky...but, you could also be the type of TA I was, where you teach the whole damn class. I have friends who were thrown into teaching classes that they had never even *taken* as undergrads, during their 1st or 2nd year in grad school. They just had to read the whole book and figure out how the heck to teach it during the 2-3 weeks between when we got our TA assignments and the first day of class. It happens. A *LOT* more than you realize.
(3) We were called TAs because we were grad students. That's the term that was always used for grad students, regardless of the specific requirements of the position/class (again, I was a "TA," even though I was the only one who ever lectured, graded, met with them for office hours, interacted with them, etc.). Jane would 100% not be called an "assistant professor," because that's the term used for PhD-holding professors who have already completed graduate school and possibly also 1 or more post-docs and are now full-on professor professors. It only gets the qualifier "assistant" because you move up to associate and/or full professor once you get tenure.
Sorry if this is way too off-topic. But as a grad student, there are some things I get frustrated about in their portrayals...but there are also clearly some things that others seem to think they're getting wrong that they're not. Which can be just as annoying.
(But the idea that a college course would have any sort of "summer reading" or "winter break reading" for a class that hadn't even started yet was bonkers.)
