Do we have to use 'for' or 'to'? Do we have to use 'a' or 'the'? Does the fun day mean the only fun day for many students? There are several fun days for many students. So, 'a fun day' for many students means one of the fun days for many students. Am I right?
Your first two examples are correct, although they signify slightly different things. The second two are wrong. You cannot use to in this context.
To say:
Sunday is a fun day for many students
tells us that many students have fun on a Sunday. It implies that they don't have fun on other days but it does not make this clear. Students may have fun on other days as well.
To say:
Sunday is the fun day for many students
compares Sunday with the other days of the week. It emphasises that the day of the week on which students have fun is Sunday and not other days.
So the difference is merely one of emphasis.
