La casa il cui giardino è grande è vicino alla stazione.

Il cui is a possessive relative pronoun meaning “whose.” It links la casa (the antecedent) to information about what belongs to it (its garden).

In Italian cui alone carries no gender or number. The preceding article (il, la, i, le) agrees with the noun that follows: here il agrees with giardino (masculine singular).

No. Che cannot express possession. If you wrote la casa che il giardino è grande, it would be ungrammatical. To say “whose garden is big” you must use il cui (or la cui, i cui, le cui).

Di cui means “of which” or “about which” and is used when the verb or adjective requires di (e.g. il libro di cui ti parlavo). For simple possession (whose), Italian uses il/la/i/le cui.

Because this is a restrictive (defining) relative clause: it specifies which house we’re talking about. Restrictive clauses in Italian are not set off by commas.

Relative clauses in Italian must follow the noun (antecedent) they modify. If you move it, it will seem to refer to whatever comes immediately before it (e.g. stazione).

The adjective/adverb vicino requires the preposition a (vicino a). Since stazione is feminine singular, a + la contracts to alla stazione.