Loose steering on 2001 wrangler

Sounds like front wheel bearings.
Does the sound go away when swaying one way or the other?
If you way left and ot gets louder it should be the right bearing and opposite for swaying right

Sounds like your turn signal switch is faulty. Did someone work on your turn signals, try to fix something, didn't know what they were doing? Was the steering wheel pulled off for any reason? May be crossed wires under steering wheel

Cgeck for play in the track bar , it goes from frame to front diff. Get a friend to move the steering wheel from left to right ( engine off ) about an 1/8 of a turn back and forth and watch for play in the steering and suspension parts. good luck.

No pump should be noisy, though if only noisy when wheels are turned all the way to either side, that is normal. Once turned to the point where the pump first begins to make noise you really don't have any more wheel movement and turning the steering wheel further does very little except cause the noise. I've found that on many Jeeps the steering stop bolts on the lower control arms are set too far in and can be turned back a bit. That may help somewhat.

check all the front end moving parts for looseness, ball joints, tie rods, upper and lower arm bushings, wheel bearings, brake mounting supports, swaybar bushings, if it makes noise and shifts it its dangerous to drive

If the u- joints are loose, yes, that would cause the front end to shake.

Your desctiption sounds like your settings are incorrect. I reccomend that an alignment shop adjust for you.

A common mistake on this type of project is steering box centerning. to test, from straight ahead, stop.., turn wheel from dead center to the stop, and measure exactly how many turns. From dead center, it must be the same both ways.

Steering boxes have an exact center setting, and get looser (so to speak) as turned right or left off of that spot. SOOO, if set to one side or the other, steering gets tighter when turning in one direction as compared to the other.

Get an alignment shop to set this up, it is common problem.

Hay I would check your sway bar in the front .The bal may have came out of the seat located under front wheel well. Also they could be just loose. Check by rocking your jeep side to side .

jack up the front wheels one at a time, turn the steering wheel all the way to the right or left and turn the wheel by hand. i think you have a bad u-joint behind the front wheel(s). if you have a bad u-joint then the wheels won't turn smoothly.

good luck