Ok guys, help diagnose my problems.

Just had a big rain and had my first chance to take my Jeep out in some of the mud pits. Here's short video of me out there.
https://www.youtube.com/watch?v=rJJYWYoDwAE&feature=youtube_gdata_player

There's three things I've noticed that seem a bit off. When turning I feel something in the steering column. Almost as if something catches somewhere inside the column. As far is the sound goes, it sounds like a popping. It was occasionally doing it before but now its more severe.

The belt in the front seems to squeak on start up. I'm sure this is a simple fix. Not sure how to elaborate on the sound of it. I hear cars with this sound all the time. It goes away after running for a little.

Now this is the one that I'm worried about the most. Every time that I'm braking loud hum coming from the front. Almost as if 2 things are rubbing that aren't supposed to be touching. It only happens when I'm braking at low speeds like 15 and below. Anything above seems normal. I'm not sure if the mud just got in the way of some grease/oil of something. But this is a pretty loud noise.

Hopefully they all are cheap fixes but I honestly have no idea. Any input is greatly appreciated.

Popping sound may be the ball joints moving a bit. Hard to say without knowing where it is comng from. Could also be worn bushings allowing movement in the front end when turning.

Squealing sound could be a glazed belt, a loose belt or a wet belt. Could possibly be a bearing in one of the accessory pullys.

The hum could be related to issue #1 with front end components moving. If you are also gettng vibration when breaking, I would say it's warped rotors.

Hope this helps a little. It's hard to diagnose noises without hearing them.

First powerwash everything good if you haven't all ready. Then I would do a full fromt end inspection, look for worn paint for signs of stuff rubing. Have someone steer the wheels back and forth while you look at everything on the front to look for slop or play. You can check your ball joints by jacking up one side at a time untill the tire just comes off, then put a pry bar under the tire and lift up, looking for seperation or play in the upper and lower ball joints.

problem 1-steering box
problem 2- wet timing belt?
problem 3 - dirt and mud on rotors/calipers?

the most serious would be the steering box, but I never worried seems like my xj always pulled a wolverine and healed itself

Could also be loose bolts in the trackbar, tie rod, draglink, etc causing a popping. Maybe bad hubs.
A wet timing belt wouldn't necessarily be the problem with the squealing. It's likely a bad serpentine belt or in need of adjustment.
Wash everything and see if the hum goes away.

Went to the car wash yesterday and power washed everything. The only thing that seemed to get better was the steering pop. The belt squealing is still there only for about 5 seconds on start up. But that hum is still there when I brake. I'm thinking about just replacing the front brakes now.

Yea like the others mentioned, disc brakes are not too happy about being mud-bathed.

Pull your calipers, un-clip your pads and wire brush them, then wipe with a clean cloth damped with rubbing alcohol. Next, use a scotchbrite pad on your rotors, and alcohol wipe them, both sides. I think you'll be pleased with the result either way. I've used the technique to fix a number of annoying disc brake related symptoms. I just love how easy it is to work on XJ disc brakes!

The pop could be from some piece of crap in your steering box. Have a friend turn the wheel while you watch and if no balljoints or links are loose, you might try there. Drain the reservoir with a turkey baster and refill. Be careful or you could end up like that guy with the sideways avatar!

Oh you can do that alcohol trick with all your pulleys and the belt too.

The short version is, mud cakes work best on stationary parts!

That pop may be from a loose bolt. Check all the bolts on your track bar, steering box, track bar mount, etc. I had the identical popping you have, I swore my steering box was toast, no movement in an front end components. Just 10 minutes ago I checked the bolts on my aftermarket drop mount for my trackbar, they were loose about half a turn, tightened em up and no more popping.

The squealing is the belt slipping on an accessory, most likely the alternator. Startup puts a big load on the battery, and the alternator has to work hard to put the charge back in. That puts a lot of drag on the belt, and causes the squealing. Don't over-tighten the belt, though. You'll kill the pulley bearings. If it still squeals with proper tension on the belt, then the belt is glazed. You can try to cure it with belt dressing, but I've never really had good luck with this as a long term solution. You really should replace the belt.

With the engine off, get someone to rock the steering wheel back and forth and watch your steering components. If something is loose, it will be evident. Look closely at the steering box, and all of the rod ends and track bar bolts.

Loud hum on braking could be a lot of things. Bad hub bearings, warped rotor, etc. Inspect everything. Lift the front tires off the ground and give the tires a wiggle. There should be no play in the bearings. If there is, replace them as a pair. If one is going bad, the other isn't far behind.