As others said, you need to give context, but I'll give it a shot (try my best). I'm going to assume that a "student day" is some kind of special day reserved for students, which would usually take place at some type of business. For example, a bowling alley might declare a "student day" in which all students get 50% off the the cost of bowling, but non-students pay full price. Are these true?if not,then why? 1>This day is a student day(noun) This would be used if you were, for example, looking at a calendar with someone. Imagine you are looking at all the days for December and January. And let's say the bowling alley designated every third Tuesday of the month a "student day." They you could point on the calendar to the third Tuesday in December and say "This day is a student day." Your friend could point to the third Tuesday in January and say, "Here is another student day in January." 2>this day is 'student day'(adj) (like this:this car is big) This implies that there is only one student day or only one day in a lengthy period. You might say "This day, July 15th, is student day." An analogy would be to say "This day is Christmas," because there is only one Christmas per year. Or you might say "November 19th is election day." Going back to your previous example, if the special day is something that happens often and regularly, like "church days," which happen every Sunday, then you'd say "This is a church day." You might say this to remind someone about what's going to happen on the day. For example, if a friend said, "Let's go to the beach on Sunday." If you were religious and never missed church, you might say, "But that's a church day." 3>which one is true and why the other is wrong>>These days are students' day /or/ these days are students' days? Both are wrong, assuming my definition of "student day" above. You would say "These days are student days." Student is an adjective that modifies "days," so only "days" has the "s" to indicate plural.

In this case, it depends what you mean by "student day" or "a student day." What is the context for these sentences?

So are they correct?and are they true? I guess u wanted to say that they are correct but not true.then why is that? You know i have a problem , im pretty acurate and fluent in english but everytime i suddenly get stucked in these little grammar points(please check up my other questions,you'll see)and i dont know what to do really. :( what should i do? im not an elementry student im pretty good but these questions disappoint me :(

You need to understand the difference between "true" and "correct". If something is true, it exists in reality. If something is correct, it has no errors. In all your examples, you need to use "correct". This is elementary English.