Learn Dutch: Ik zoek haar pen. - I am looking for her pen.

The Dutch verb zoeken translates to "to look for" or "to seek". You don't need to add a separate word for "for" (like voor) because that meaning is already built into the verb itself.

Does the possessive word haar (her) ever change its ending to match the noun it describes?

No! In Dutch, singular possessive words like mijn (my), jouw (your), zijn (his), and haar (her) never change their spelling to match the noun. It stays exactly the same whether it comes before a de word or a het word.

The English translation says "I am looking", but Ik zoek looks like the simple "I look". Why?

Dutch usually doesn't use an "am + -ing" structure like English does. The simple present tense Ik zoek can mean both "I look for" and "I am looking for". The context makes it clear that you are doing it right now.

I remember seeing the word haar used to mean "hair". Is it the exact same word?

Yes, it is spelled and pronounced exactly the same! Haar can mean the possessive "her" (as in haar pen), the object "her" (as in "I see her"), or the noun "hair". In a sentence like this, it is easy to tell that it means "her" because it comes right before a noun.