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Sounds like your transfer case is working, maybe the vacuum system to lock your hubs is not working. Try manually locking the hubs and check to see if the front wheel starts working. No clue on the shifting.
Start with the simple. How many miles, when was the last fluid change. Was the change a drain and fill or a pan drop filter change?Is it chipped? Do you tow? Do you have gauges. Is the fluid nice and pink? Does the fluid have even the slightest hint of burnt smell.
Anytime RR. If the fluid is clean and at the right level I'm hard pressed to say change it out at this point. Have you had it on a scanner capable of pulling transmission codes? This is where I'd go next.
Could be excessive build up of metal deposits on the gear solenoids which causes erratic shifting, can even put it in park and grenade the trans. Was a recall on 2011-2013 F150's with the 6R140. Same trans basically in the super duties. The fix if that's the case is a different solenoid valve seal, plus fluid and filter change. Trans fluid change is every 65,000 miles I believe.