Yes. I think its faster (by a tiny bit) to just grind mob. Tho i belive at some point youll hit some mobs that are annoying and will make you have a tiny break inbetween pulls.
Personally i wouldnt just grind mob through multiple levels. Ive just done it between 53-54, and i got rather bored with it after that.
Quests will shake it up and make the game more fun, rather than just killing mobs.
Gold .. I think its better to just grind mobs? I do get 1-2g per quests, sometimes with a random quest reward worth 50s-5g. Tho mobs have the random chance to drop good loot that can be sold on AH (personally got a Destiny between 53-54). Tho, you do still have this chance when youre just doingt quests.
In my opinion.
If this is your first character (like myself). Id just enjoy the leveling and not think about how long it takes. Do some quests and grind now and then to catch up with zones. Ive spent 8 days 12 hrs in /played to get to 55. Mainly through quests, and getting camped for a few hours by 60s here and there