Learn German: Können Sie das Formular bitte ausfüllen?

You are right, ausfüllen (to fill out) is a separable verb! However, because this sentence uses the modal verb Können (Can), the second verb gets pushed to the very end of the sentence in its full, unseparated dictionary form (the infinitive). If you didn't use a modal verb, you would separate it: Füllen Sie das Formular bitte aus.

Why does the sentence start with Können?

This is a yes/no question. In German, to turn a statement like Sie können... (You can...) into a question, you simply swap the subject and the conjugated verb. So it becomes Können Sie...? (Can you...?).

Why is Sie capitalized in the middle of the sentence?

The capitalized Sie is the formal way to say "you" in German. Since filling out a form is usually something you are asked to do in an official setting (like a bank or doctor's office), the formal Sie is the natural choice. If you were asking a friend, you would use the informal du: Kannst du das Formular bitte ausfüllen?

Is das Formular in the nominative or accusative case here?

It is in the accusative case because it is the direct object—the thing being filled out. Luckily, neuter nouns like das Formular don't change their word for "the" in the accusative case, so das stays das.