Deprime then clean because clean brass is next to Godliness. Everything works better when it is clean and the same goes for brass. I always deprime then clean. Who wants the gunk from fired primers mucking up the cleaning solution. My 2 cents for cleanliness. LOL!
I don't deprime pistol brass before tumbling because it's one less step to complete and saves lots of time.
I dry tumble. I always clean then de-prime. Been a long time since I've even worried about cleaning primer pockets
Pistol, NO. You don't need lube the brass with carbide dies.
Rifle, Yes. Lube, de-prime, wet tumble. It cleans the brass and washes off the case lube at the same time.