hey and welcome
1- the main grind is titles, think of them as achievements, they include a variety of pve and pvp content grind throughout all campaigns (the pve one is not redondent, you basically need to clear everything once in NM and HM, though farming is needed for some and also take advantage of double points week bonuses)
2- big is subjective, but i guess you can say all campaigns combined makes it pretty big, exploration is one of the titles i mentioned
3- kamadan american district is the trading hub and "main city" it is the first big city in Nightfall
4- the hall of monuments is a small area in Eye of the north in which you dedicate (make it untradeable in the future) certain weapons, minipets and also your armor, your hero's armor and your titles. doing so gives you rewards in Gw2
gl and enjoy the game