Learn Icelandic: Við erum trúlofuð og elskum hvort annað.

The phrase for "each other" when exactly two people are involved is hvor annar. The first word matches the subject's gender. Because the couple is mixed-gender (shown by the neuter plural adjective trúlofuð), we use the neuter singular hvort. The second word takes the case required by the verb. Since elska (to love) takes the accusative case, we use the neuter accusative annað.

Why do we use a form of hvor here instead of hver?

Icelandic makes a strict distinction based on the number of people involved. If there are exactly two entities (like an engaged couple), you must use hvor annar. If there are three or more people, you use hver annar.

Why does the adjective trúlofaður (engaged) take the form trúlofuð here?

Adjectives must agree with the gender of the subject they describe. The pronoun við (we) refers to the couple. When referring to a mixed-gender group (like a man and a woman), Icelandic always uses the neuter plural form of the adjective, which is trúlofuð.

Could we just say við elskum okkur to mean "we love each other"?