Is "How much are you done with the assignments?" grammatically correct? If not, How can it be rephrased?
In the question "How much are you done with the assignment?", the verb "are" and the prepositional use of "with" seem out of place. "Are" is definitive when it feels like you want to express ownership and "with" indicates either being against something, such as "He fought with his brother.", or in accompaniment such as "He went with his brother to the store."
You most likely want to use "have" instead of "are" in this case, but the replacing "with" can change the meaning so that it's either an assignment that's assisting the subject to his goal, or the assignment's accomplishment is the goal.
Choice 1: the assignment is assisting the subject to accomplish his goal. Replace "done" with the word "accomplished" in your mind when reading the following:
How much have you done through the assignment?
Choice 2: completing the assignment is the subject's goal. When reading the following sentence, replace "done" with the word "completed" or "finished":
How much have you done of the assignment?
Note that in this second example, by placing the activity before the object (the assignment) you are placing a slight emphasis on the action. You can make the assignment have slightly more focus on your sentence by placing it before the action like this:
How much of the assignment have you done?