Which one is more correct, if everybody knows that I am talking about all the students in a specific classroom.
assignments must be done by all the students
assignments must be done by all students
assignments must be done by the all students
Every one of the group of students, who are defined either implicitly or by a previous statement, must do the assignments.
As well as being identified by a previous statement, we could go on to define the group; "…by all the students who are doing the advanced course".
Every student must do the assignments.
This could mean the same thing as the first, or not, depending on whether we've a context that defines a particular group, whereas one that gives us a different interpretation of "all students" (generally all taking a particular course, all in a particular school or college, etc. would be obvious from context).
Generally, if we don't have such a defining statement, we'd favour this second. If we do, we'll favour the first.
Ungrammatical, and meaningless.
The first two are grammatical, but the third isn’t. Normally, either of the first two will be suitable, but the choice may depend on the context.