Learn French: C'est le refuge du guide. - This is the guide's shelter.

This lesson is about ne... aucun(e). How would I use that here to say "This is no guide's shelter" or "This is the shelter of not a single guide"?

You would say Ce n'est le refuge d'aucun guide. Notice how the negative adjective aucun replaces the definite article le before the word guide. Because the le is gone, the contraction du (which is de + le) breaks apart, leaving just d' before the vowel in aucun.

Why do we use C'est here instead of Il est to mean "It is" or "This is"?

You must use c'est because the phrase that follows is a noun introduced by an article (le refuge). You generally only use il est (or elle est) when describing something with a standalone adjective, like Il est grand (It is big), or an unmodified profession, like Il est guide (He is a guide).

Why is it du guide instead of just de guide for "the guide's"?

To show possession in French, you literally say "the shelter of the guide." This requires the preposition de (of) plus the definite article le (the). Whenever de and le are next to each other, they are forced to combine into the mandatory contraction du.

Is the noun always masculine?