Learn Arabic (Modern Standard): لم أهن زميلة قط. - I have never insulted a female colleague.

قط means "never" specifically for past events. Since the negative particle لم places the meaning of the verb in the past, you must use قط. أبداً is used to mean "never" in the future (for example, with لن).

The verb for "I insult" is usually أُهين (uheen). Why did the ي (yaa) disappear in أهن?

The particle لم forces the following present tense verb into the jussive case (majzoom). This puts a sukoon (no-vowel mark) on the final letter ن, which creates a forbidden sequence of two unvoweled sounds: the long vowel ي and the silent ن. To resolve this, the weak middle letter ي is dropped, resulting in أُهِنْ (uhin).

Should I pronounce the final vowel on قط if it is the last word in the sentence?

Yes. Normally, you drop the final short vowel of a sentence in Arabic. However, قط is an unchangeable (mabni) word that always retains its final damma (u) ending. Therefore, it is always pronounced qaTTu, even at the end of a breath.

What case ending does زميلة (female colleague) take in this sentence?

It takes the accusative case (mansuub) because it is the direct object of the verb. If read with full endings, it is pronounced زميلةً (zamiilatan) with a tanween fatha.