Learn French: Le cygne fait son nid ici. - The swan makes its nest here.

You would say C'est ici que le cygne fait son nid (It is here that the swan makes its nest). Even though ici is an adverb of place rather than a prepositional phrase, it works exactly the same way with the C'est... que structure to add strong emphasis to the location.

What if I want to emphasize that it is the swan making the nest, rather than the location?

You would change the structure to emphasize the subject: C'est le cygne qui fait son nid ici. Notice that you must use qui instead of que because le cygne is the grammatical subject performing the action.

Is faire the only verb used for a bird making a nest?

You will also frequently see construire (to build) or bâtir (to build), as in le cygne construit son nid. However, faire son nid is a very common and natural collocation in French, much like "making a nest" in English.

Since cygne ends in an 'e', is it a feminine noun?