Learn Arabic (Modern Standard): هل تلك المرأة ممرضة؟

تلك is the feminine word for "that", used here because المرأة (the woman) is a feminine person. If you were talking about "that man", you would use the masculine word ذلك.

Why does المرأة have "al-" (the) attached to it? Doesn't that mean "Is that the woman a nurse?"

In Arabic, to say "that noun", the noun must have the definite article ال (al-). So تلك المرأة translates as "that woman" as a single phrase. If you left off the ال and just said تلك امرأة, it would become a full sentence meaning "That is a woman".

Why does the word for woman, المرأة, look so different from the word for "a woman" (امرأة)?

The word for woman is a unique exception in Arabic! When you add the word for "the" (ال) to "a woman" (امرأة), the spelling changes and it becomes المرأة. It drops its original first letter.

Where are the words for "is" and "a" in this sentence?

Arabic does not use a "to be" verb like "is" in present-tense sentences, and there is no Arabic word for "a" or "an". You simply put the subject (تلك المرأة, that woman) right next to her profession (ممرضة, nurse) to make the sentence.