Well, don't know about size but someone on here will. You can get arrivals and departures on the day http://flybrighton.com/live-information/flight-arrivals-departures/
What is the maximum size aircraft permitted to land there - Airbus A318 https://en.wikipedia.org/wiki/London_City_Airport
Latest Departure Times - Could be misunderstanding but they don't seem to be later than 9PM https://www.londoncityairport.com/departures-and-arrivals