I had a course in which the instructor let the markers make the midterm marking scheme and had students ask the TAs to resolve any marking issues instead of talking to him, though the instructor provided sample answers. As far as I know, many TAs are inexperienced and I think leaving the job of making marking scheme to TAs may be too much for them. IMO, making marking scheme should be the instructor's duty. I don't know if it is common in university.
This might vary by country, but in the US, if the graders are undergraduates--which shouldn't be the case for midterms--then I would say that it's unusual to allow them to decide on the grading scheme. If the graders are grad students, it's quite common. At many schools even first-year grad students are the instructor of record for a course.
From my personal experience, both as a student and TA I would say that this is quite common in the US, particularly in large, lower level courses. Many professors find such courses boring to teach and will hand off as much as they can to the TAs. For some courses, the TAs may even give regular lectures.
As a TA, it's not all bad though. They often write portions of or all of the exams, which allows them to make sure students have a firm understanding of the most important material. They also likely have a better grasp of where students are struggling and will focus on those areas during recitations or review sessions. Students tend to feel more comfortable approaching them, assuming they're doing their job appropriately.
Regardless, if you truly feel like the TA is marking unfairly and isn't doing an appropriate job explaining their grading scheme when you ask them about it, you should take it up with the course instructor - particularly if others students are voicing concerns over the same issues.
As someone not from the US (I'm a PhD student in Hong Kong) - yes, here too. TAs are only graduate students, however. Before we were allowed to take on TA work, we had to take a "Certificate in Teaching and Learning" course where it was explicitly shown to us how to create a good grading rubric and grade fairly, among other things.
Don't think that everything the instructor does will automatically be better. TAs have more time to spend on the course, usually. In my case the professor is so busy that practically all his sample answers, when he does have time to make them himself rather than leaving it to me, contain multiple errors! (Of course I also make plenty of mistakes, but they usually become apparent while grading and get fixed before the students see them.)
In my experience (two large state universities in the US) this is unusual. My experience was that the TA or TAs graded the midterms and finals, but the professor reviewed the exams before the grades were officially recorded and before the exams were returned to the students.
Now, about the grading scheme. For exams, the professor gave the TA(s) the grading scheme, which had been built into the exam during the design phase. For homework:
For a large course with multiple TAs, the more experienced TA(s) would set up the grading scheme, and the less experienced TA(s) would ask a more experienced TA for guidance when unsure.
For a smaller course with just one TA, the instructor often provided guidance. If not, the TA could set up a grading scheme, and if in doubt, could check with the instructor.
Tip: If I were in your shoes, I would request an assignment, for next semester, to a large course, where you'd be part of a TA team, and would learn by doing, alongside at least one more experienced TA.