Learn Arabic (Modern Standard): لم أر أخي مؤخرا.

The negative particle لم (did not) forces the following present-tense verb into the jussive case (majzoum). For verbs that end in a weak letter like an alif maqsurah (ى), this grammatical state is shown by completely dropping that final weak letter. Therefore, أرى loses its last letter and becomes أر.

How should I pronounce أر here if the final letter is missing?

Even though the final alif maqsurah is dropped in writing, the short vowel (fatha) on the letter ra' (ر) remains. It is pronounced أَرَ (ara) with a short 'a' sound at the end, not as a clipped 'ar'.

Could I say ما رأيتُ instead of لم أر?

Yes, you can. ما رأيتُ uses the negative particle ما with a past tense verb, while لم أر uses the particle لم with a present tense verb. Both translate strictly to 'I did not see' and are perfectly correct in Modern Standard Arabic, though لم is generally more common in formal writing.

What is the grammatical function of the ending on مؤخرا?

The double fatha (ـًا), known as tanwin fatha, marks the accusative case (mansoub). Here, it is used to turn the word into an adverb. It comes from the root أ-خ-ر (meaning late or delayed), so adding the tanwin transforms it into the adverb 'lately' or 'recently'.