You could remove the third with the axle housing bolted in the trackick.....but it would be a big PITA. Much easier to remove the front axle assembly (like you have done) and take it apart.
Yes, all the bolts that you circled in yellow have to come out (there should be 8 of them). Pay attention to the bolts, because 2 of them are different than the other 6 (the 2 "oddballs" take a 14mm wrench/socket to remove them, so it is pretty obvious which ones they are).
The axle circled in green has to come out too. The axle can sometimes "stick" in the housing, use a block of wood up against the 3 holed flange, to protect it, and use a BFH (big F'n hammer) to smack the wood block really hard and the axle shaft will pop out. Stand with your foot on the side of the thirdmember, to keep the axle housing from sliding when you are smacking the axle flange.
The big nut on the end DOES NOT need to come out to remove the complete third. It holds the flange on the end of the pinion gear and only has to be taken off if you are changing the pinion flange, removing the pinion gear, or replacing the pinion bearings (basically anything to do with the pinion).
IIRC, you are just swapping complete thirds out, so simply remove the 8 bolts that hold the third in the axle housing, remove the axle shaft, then the third will come out (it may be kinda "stuck" in the axle housing....since it has sealant on it to keep the gear oil from leaking out)......if it is stuck, just turn the axle assembly so the pinion flange is sticking straight up in the air, stand on the long axle tube and grab onto the pinion flange and rock the third back and forth and it should pop loose......if it doesn't use a block of wood against the edge of the thirdmember (just under the pinion flange) and gently, but firmly, tap it with a hammer.