Learn Arabic (Modern Standard): كتبت الأستاذة جملة طويلة.

In writing, كتبت (katabat) ends with a sukoon (no vowel). However, because الأستاذة starts with a connecting sound followed by the vowelless consonant l, you get two vowelless consonants in a row. To fix this, Arabic adds a helper kasra (an i sound) at the end of the verb. It is read aloud as katabati l-ustaadha.

Why doesn't the direct object جملة have an extra alif added to the end?

Normally, when an indefinite noun is the direct object, it takes the -an sound (tanween fatha) and adds an extra alif to the spelling. However, because جملة ends in a taa marbootah (ة), the tanween is written directly on top of the letter (جملةً) without adding the extra alif.

What case ending does the adjective طويلة take in this sentence?

It takes the exact same ending as the noun it describes: an -an sound (tanween fatha). In Arabic, adjectives must match their nouns in gender, definiteness, and case. Since جملةً is an indefinite direct object in the accusative case, the adjective perfectly mirrors it to become طويلةً (Tawiilatan).

Is there a difference between using أستاذة here instead of معلمة?

Yes. While both translate broadly to teacher, أستاذة is typically used for a university professor, a college instructor, or as a title of high respect for a professional. معلمة usually refers specifically to a school teacher at the primary or high school level.