I think it is likely some lower quests will be added, from time to time in the patches they have added some quests. But I am not sure, since the expansion is centered in Ishgard.

I used the quests to level (with dungeons too) only the first class I leveled, since it's the only class you have at that moment and you use it all the time. Now the low level roulette and guildhest roulette, together with the challenge logs (try to make sure you finish the challenge with the class you are leveling) are the best ways to level up. Maybe some FATEs (or levequests) if you just need some exp to level up and have a better quest or dungeon available, or while you wait the queue if you are leveling a DPS. The hunting log also gives exp.