I heard somewhere (not sure where) that the Royal Chapel and Cathedral are only open in the morning. Is that true? What are the hours now for the coming months into 2017?
No, as far as I can tell both are open in the AM and PM - but the chapel at least takes a siesta in the middle of the day. Maybe this is the basis for what you read?
Chapel website says 10 - 1:30, and then 3:30 - 6:30, shorter hours on Sundays
http://www.capillarealgranada.com/index.en.html
Cathedral says it is open 10-6:30, except Sunday when it is only open in the afternoon (there is mass in the morning)
website in Spanish but is pretty understandable
http://catedraldegranada.com/precios-horarios-de-la-visita/