Wheel Bearings:
Your description sure does sound like front bearing/s going. Have you (OP) replaced front hubs before? It "can be" a lot bigger and frustrating job when they get rusted in place. For a lot of guys they look back and wish they'd paid a shop to do them. They can be a real bugger. But if you've done them before, then yeah, go ahead and do them. Buy some good SKF or Schaffler hub assemblies. RockAuto has good prices on them. I would also replace both if your finances allow. I've had too many fail close to each other (but not always) and then you need to go through the whole job a 2nd time. Once you have all the tools out (weather you or the mechanic) it goes faster to do both. But yeah, if finances are tight, then I can see doing one at a time. The other may last a yr... or even 3 years. Or 6 months. If you're doing them in your driveway, having fail in the winter would be the worst.
I just ordered two front hubs for my truck. I also have one failing ironically. Driver's side. I'm going to replace them both ..I just don't want to do the whole job a second time and knocking on the door of 180k. On my truck the hub assembly started to make a whirling sound and then went away for a month. Then I wasn't sure if I was hearing something else. I've had it where a failing front hub can be in a failing mode for many months. However in my Ram, just a couple days ago, coming home from the Home Center, suddently the hub noise became suddenly VERY LOUD out of the blue. I had to drive 50mph or under on the way back, as it was also vibrating. You can 'feel' the bearing is 'rough' rotating the hub by hand. So sometimes they can creep up on ya too. If your truck is a DD, you probably don't want it to be suddenly down. If you do replace it on your own. I think Autozone rents an axle 'pusher' which is a lot better than banging on the axle stubs with a maul, like some guys do.
Rear Differential:
As for the rear diff, sounds like your mechanic is talking about a loose pinion? I don't think he can say what the longevity is just by seeing the 'play'. Did the mechanic attempt to tighten the nut? I would definitely do that first. The bearing there is a tapered bearing. Tightening the nut should remove the freeplay. Sometimes the nuts can become loose, or maybe it was put on semi-loose when new? Remove the driveshaft and a snugging up is worth a shot. If there is a serious issue, you'll hear noise and know you need to take things to the next step.
Yes... I know there is a specific 'correct' way guys will chime in & say you
MUST tighten the pinion with a new crush-sleeve, etc. But ..not really ...in a case like this. At this point, you're trying to see if tightening to, say, 90 or so ft/lbs removes the freeplay. I've done several (and I know other people who have too), just snug up the nut and there you go. Drive a bit then recheck. Put the vehicle in N, (block the tires) and check it again periodically. If it sounds fine and still tight, order a new pinion nut and replace the old one. Long term, if there is continued looseness or noise, you should call up a "differential and driveline place" asap who does this stuff for a living, tell them your story, and have them take a look. If nothing else pay for an 'inspection'. If it comes back 'good' then you have peace of mind. If they find something, they're the better guys to give a long-term assessment. Sooner is definitely BETTER than later with driveline issues. Things get real costly when they went on too long, start to fail and/or seize up. But start by snugging the pinion nut and see what happens. You ought to be able to do that in 20 minutes.
Transmission:
The tranny, IDK what he's seeing, and not being there, not sure how he can make a lifespan determination. I agree with others to have the fluid changed. And DO it the RIGHT way... by jacking up the rear wheels and verifying the fluid level. That you should be able to do also. It's been shown here over the yrs most shops don't know the correct method of final-checking (verifying) the fluid level. And most shop techs prefer to work on a hoist, not crawling around on the floor working around someone else's hot exhaust. The fluid level needs to be right-on. Verify that yourself. And the type of fluid. Use the right and good fluid. Then you can know it was done properly. I would personally use Mopar or ZF fluid rather than Penzoil or somesuch brand. Then you don't have to worry about different additive packages causing any operational flukes (that can happen). Our small town Ram dealer will fill milk jugs cheap out of their bulk trans fluid barrel (ask your local small dealer PARTS dept).
It's always better to replace the fluid. If a tranny problem develops, it was on borrowed time anyway. Worst case you could look for a used one from a wrecked truck.
Good luck!!
