My turbo has not gone bad. It is not common for turbos to go bad (I currently have 5 turbo vehicles with the F-150's 72,000 miles being the youngest; none of my vehicles has ever lost a turbo). That said, they can go bad for many reasons. Variable vane mechanisms can freeze up. Bushings and bearings can fail. Seals can fail. Some turbos are more prone to failure than others, I have read of at least a few turbo failures on this forum. You can do a search to find them.
As for "the dealership offers...a warranty via a 3rd party"; it would normally cover something like that depending on the fine print, but it is not clear whether you purchased this warranty or if your truck came with this warranty. Take a look at your purchase agreement.
I don't know which end of the air intake hose the crack is located on, if it's at the turbo end, it is highly unlikely that the guys who changed the air filter caused it. Even if it is cracked at the airbox side, I don't think the air filter guys would damage it. I don't see how being dirty plays into anything. Assuming we are talking about he hose from the air box to the turbo, it is possible that it got brittle from the heat of the turbo and failed when they tried to pull it off for turbo replacement. If so, that is a tough call regarding who is responsible for the cost. Regardless of how you sort that one out, I would be looking at what they are quoting for the pipe. The air intake pipe is a $340 part. It appears to be held in place by one bolt and a hose clamp on either end. I would also assume that it gets removed and reinstalled during a turbocharger replacement. If that is the case, Ford warranty already paid the labor to R&R that part (or at least disconnect it from the turbo end, which would be the bulk of the labor). From the price you list, it sounds like they are trying to quote an hour of labor to do this, which would be about right if they had to remove the fender liner to access the lower hose clamp. That would already have been done if they replaced the turbo, however. I would certainly question them on labor for the hose..
As for "the dealership offers...a warranty via a 3rd party"; it would normally cover something like that depending on the fine print, but it is not clear whether you purchased this warranty or if your truck came with this warranty. Take a look at your purchase agreement.
I don't know which end of the air intake hose the crack is located on, if it's at the turbo end, it is highly unlikely that the guys who changed the air filter caused it. Even if it is cracked at the airbox side, I don't think the air filter guys would damage it. I don't see how being dirty plays into anything. Assuming we are talking about he hose from the air box to the turbo, it is possible that it got brittle from the heat of the turbo and failed when they tried to pull it off for turbo replacement. If so, that is a tough call regarding who is responsible for the cost. Regardless of how you sort that one out, I would be looking at what they are quoting for the pipe. The air intake pipe is a $340 part. It appears to be held in place by one bolt and a hose clamp on either end. I would also assume that it gets removed and reinstalled during a turbocharger replacement. If that is the case, Ford warranty already paid the labor to R&R that part (or at least disconnect it from the turbo end, which would be the bulk of the labor). From the price you list, it sounds like they are trying to quote an hour of labor to do this, which would be about right if they had to remove the fender liner to access the lower hose clamp. That would already have been done if they replaced the turbo, however. I would certainly question them on labor for the hose..