Learn Polish: Gdzie jest mój portfel?

In Polish, words like "my" must match the gender of the noun they describe. Portfel (wallet) is a masculine noun (you can often guess this because it ends in a consonant), so we use the masculine form mój.

Why doesn't the word portfel change its ending here?

It stays in the Nominative case, which is the basic dictionary form. This is because the wallet is the subject of the sentence. Even though you are the one looking for it, grammatically the wallet is the thing that "is" somewhere, so it doesn't need to change case.

Is the word order strictly set, or could I ask "Gdzie mój portfel jest?"

Polish word order is quite flexible, so you would definitely be understood! However, it sounds much more natural to put the verb jest (is) in the second position in the sentence, right after the question word Gdzie.

I remember learning skąd for "where". Why do we use gdzie here?

Gdzie is used to ask "where at" or the current location of something. Skąd specifically means "where from". You would use skąd if you were asking where someone is from, or where they bought the wallet, but to just find its location, you need gdzie.