"Can a Buddha experience weariness and annoyance ?"
Yes, His "body" still can. The World Honored One attained freedom from samsara, not a steel body that is impervious to physical pains. Due to the big limitation of common expression language, we need to interprete the Buddha's common expression of "there would result but weariness and annoyance to me" to mean the crude Five Aggregates, not "Himself", for an Enlightened One has completely eliminated all conceits about "I", "mine", and "myself".
"Bear with it, brahman! Bear with it!"
Same idea as the first question, just common language expression. As a matter of fact, I'd be surprised if I saw the Enlightened One saying nothing when seeing His noble disciple coming back with "head broken open and dripping with blood, his bowl broken, and his outer robe ripped to shreds"!!