if it´s more as a treat thing.. it should do no harm.. would be better if it were plain chicken.. without preservatives and all the other stuff used when making the outer crust and all.. but like I said as an occasional treat it should be fine.. same as bananas.. bananas are good for potassium..

about the limping.. maybe check to see if he has anything stuck into his paw.. or for cuts.. maybe he injured himself or got stepped on.. a bad jump.. who knows..

the coughing.. how long has it been.. is it constant.. or when does he coughs more.. he could be sick.. he could have something in his throat.. he could have a trachea injury..

and good luck on your exams