Steering wheel feels like it wants turn itself when driving and front suspension rattles when goig over bumps, grooves on the road.

Generally, no. However, if your wheels are toed out, the tires catch grooves in the road and wants to wander over the road. It may feel like "play" in the steering. Play in the steering is usually caused by bad tie rods and they let the wheels wiggle while driving and the effect is a car that wants to wander over the road.

First, have the tire inspected before you do any expressway driving. you could have a damaged tire with a tread or internal ply separation. second, inspect the front shock absorbers, it sounds like the left front shock has failed and lost its hydraulic fluid. third have the front steering linkage and front suspension checked for worn or loose tie rods, idler arm, ball joints and stabilizer bar links. do this ASAP as you don't want to have the tire fail or any parts break while you are driving!

check steering ball joints for wear. Check for loose wheel bearings. Check front end suspension

check the steering knuckle bearings ( top and bottom ) If you have a front axle as in cruiser or bronco ( not independent suspension) there are tapered roller bearings top and bottom on both sides . These bearings do not rotate as normal and get brinnelling grooves that will tend to lock up the steering as the rollers have to roll in and out of the grooves.

Check cv joints. check wheel bearings.. Check wheel nuts are tight and are tightening up on the center part of the wheel

If the 4wd was engaged on dry pavement you would have a difficult time making a turn because the front tires would be turning at the same time.
If the bump or vibration is felt when you are driving down a straight road I would agree with the ball joint or other suspension theory.
I will note here that Jeep Cherokee came with two different kinds of 4wd, one version can be driven on dry roads when engaged.

Could one shock be bad? Causing a difference in bounce return rate? I would crawl under suspended car and check all suspension bolts. Are your bushings in good shape? If one is chewed up or missing then this would cause that misalignement. What kind of suspension do you have? Solid axle or independent susp? I don't know if your car is front or rear wheel drive. I'm guessing front wheel drive.

It is common for the front sway bar links to wear out. This can cause a sense of looseness, with a slight rattle in the suspension when going over bumps, or when making turns. They cost about $60 a pair at auto supply stores, and can be changed in about 1 hour. There was also a GM technical service bullitin on this vehicle in regards to the steering column which is also a possibility, as well as one regarding loud knocking sounds related to the front strut spring cups.

Hmmm, it's normal for the ride in a 4wd to feel "different" they feel like they wallow a bit in turns and shudder a bit over bumps compared to a car, but it should not be jumping all over the road! try the old suspension test, go to each corner of the car and give it a good hard push down and let go, if the car comes back up and setles, all is good, if it doesn't go down or if it bounces up and down, the shocks/struts need replacing. Also try grabbing each of the front wheels and trying to move them left to right, then up and down, if there is any clunking or movement (without the steering wheel moving) there is a problem. left and right wobble indicates steering problems, up/down wobble indicates a wheel bearing broblem.

I would look at changing out your bushes. do both sides as if this happend on the right you can bet your bottom dollar that the left will soon go as well. While you are at it check your shockabsorber mounts.