Learn Hardcore Icelandic: Svefnherbergið mitt er lítið en hlýtt.

In Icelandic, nouns get a definite article as a suffix. For neuter singular nouns like svefnherbergi (“bedroom”), you add -ið to make it “the bedroom.”
So svefnherbergi = “a bedroom,” svefnherbergið = “the bedroom.”

Why is the possessive pronoun mitt used here instead of minn?

Possessive pronouns agree in gender, number, and case with the noun they modify. Svefnherbergi is a neuter noun. Neuter singular “my” is mitt.
Masculine would be minn, feminine mín, plural mín.

Both adjectives lítið and hlýtt end in -t. Why?

Adjectives agreeing with a neuter singular noun in the nominative case take the ending -t.
The base forms are lítill (masc), lítið (neut), lítil (fem); hlýr, hlýtt, hlý.

What does the conjunction en mean? Could I use og instead?

Here en means “but,” contrasting small vs. warm: “small but warm.” Og means “and” (simple addition), so “lítið og hlýtt” would be “small and warm” without the sense of contrast.

Why is the possessive pronoun placed after the noun (svefnherbergið mitt) rather than before?

When you use the definite suffix on a noun, the possessive pronoun follows it. You could also say mitt svefnherbergi (my bedroom) without the suffix, but the more natural way to say “my bedroom” with the definite article is svefnherbergið mitt.

Could I rearrange the word order, like Mitt lítið en hlýtt svefnherbergi?

No; Icelandic prefers Subject–Verb–Predicate for sentences like this. To describe the bedroom you can place adjectives before the noun (mitt litla, hlýja svefnherbergi = “my small, warm bedroom”), but if you want the definite form in a full sentence you use svefnherbergið mitt er lítið en hlýtt.

How do I pronounce the letter ð in svefnherbergið?

ð (called “eð”) is pronounced like the English “th” in this or that—a voiced dental fricative.