Which of the following is correct?
1) Sections X to Y
2) Section X to Y
3) Section X to Section Y
4) Sections X and Y
5) Section X and Y
More importantly, I can't recognize the part of speech of "Section X" or any one of the above examples. Is there any grammar rule for the construction of such structure or is it just like some idioms that you can only follow?
There will probably be an element of following a manual of style, especially if writing for a publication or in academia, but generally you would use the plural sections unless you explicitly say each thing is a section. For example:
See sections 1 through 7.
See section 1 through section 7.
You can replace through with a number of other prepositions or conjunctions, including and, to, or, with, and so on, depending on what exactly you want to say.
That does not mean that your other sentences are incorrect. There are contexts where Y in your sentences might not be a section number. For example, consider that section 10 is 6 paragraphs long, but only the first 3 are relevant:
Read section 10 to paragraph 3.
In this case, the sentence is an instruction to only read up to paragraph 3 of section 10. This sentence is also ambiguous, as it can also be interpreted as an instruction to read from section 10 to paragraph 3, with paragraph 3 not necessarily being part of section 10.
Read section 10 and paragraph 3.
In this case, section 10 and paragraph 3 are explicitly separate, and the reader is instructed to read both of them.
As for the structure of "Section 5," I believe 5 may be a postpositive noun modifier. That is, a word which changes the meaning of (modifies) a noun and is placed after (post) the position of the noun it modifies.
