Learn Dutch: Passen deze schoenen?

Because schoenen is plural! When you want to say "these" for any plural noun in Dutch, you always use deze. The word dit means "this" and is only used for singular het words.

Is the singular word for shoe a de or het word?

It is de schoen. Since it is a de word, you also use deze for the singular form to say "this shoe" (deze schoen). But remember, even if the singular noun were a het word, the plural "these" would still be deze.

Why does the sentence start with the verb passen? Where is the word for "do"?

Dutch does not use a helper word like "do" to ask questions. Instead, you just swap the subject and the verb. The statement "These shoes fit" is Deze schoenen passen. To turn it into a question, you move the verb to the front: Passen deze schoenen?

Why is the verb passen and not past?

The verb has to match the subject. Because deze schoenen (these shoes) is plural, we use the plural verb form, which in Dutch is just the full infinitive word: passen. If you were asking about just one shoe, you would use the singular form: Past deze schoen?