Learn Icelandic: Við getum sofið hvar sem er.

Hvar refers to a stationary location (where at), which makes perfect sense with the verb sofið (sleep). If the verb involved movement toward a destination, like going or driving, you would need to use hvert sem er (anywhere / to wherever).

Does the phrase hvar sem er change its form depending on who is sleeping?

No, it stays exactly the same. While phrases like hver sem er (anyone) decline for case and gender because hver is a pronoun, hvar is an adverb. Adverbs do not decline, so hvar sem er is a fixed phrase regardless of the subject or the case of the sentence.

Why is the verb sofa written as sofið rather than the infinitive?

The verb getum (can or are able to) always forces the main verb that follows it into the supine form (sagnbót). For the verb sofa, that form is sofið. This often trips up English speakers who are used to following the word can with an infinitive.

What do the words sem er literally mean at the end of the sentence?

Literally, hvar sem er translates to where that is. In Icelandic, combining a question word with sem er is the standard grammatical formula for creating free-choice words like anywhere, anyone, or anything.