[chryuop]

The thing of the なの is easily explanaible. Nouns and na-adjectives cannot have a predicative form on the contrary of true adjectives. Knowing this, you will understand that 学生 is not a proper grammar, but it must be 学生だ. Grammatically when you have だ preceeding の it becomes な (maybe a native speaker can be more precise on the reasons).

(Just to complete more what Lucas' s point was).