My 1998 Chevrolet c1500 4x2 5.7 v8 left front wheel makes, what could be the problem. I just had a watepump replaced a few days ago, could this have anything to do with the wheel or brake getting too hot?

need to check your axles, and if it's not that check your brake pads/wheel bearings.

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If you swerve the car back and forth and the sound dissapeers when swerving to the left( reducing the weight on front left tire) this could indicate a wheel bearing problem

The most common reason for a humming noise in the front area of your car would be a wheel bearing noise. I would start by having the wheel bearings checked.

There are two ways to check the bearings, one would be to jack wheels of the ground and check for free play in wheels, the other would require having a tech test drive the car, a good test drive by a tech can tell you if it is a wheel bearing problem.

A wheel bearing noise will get louder as the speed increases and the tone will change if the wheel is turned left or right.
You can try this test yourself, get car up to speed of noise and then listen as you turn wheel to left and then right and if the tone changes then i would suspect the bearing and next step is to find out which one, this would need to be done on a lift. good day

sounds like your cv joint is bad . Have it replaced sooner rather than later as when it fails, you'll be stuck somewhere and will need a tow.

Having owned a trans shop years ago,I would suggest you never engage the front wheels on a 4x4 or all wheel or run any vehicle, off the ground, that has drive axles and cv joints.
You may not have any problems,but without the wheels on the ground, it seems you do.
There is no true 4x4. Only one wheel drives in the front and rear,on any vehicle,except in theory.
Keeping in mind, that most veh have ABS Systems, that control drive and braking systems,your most likely disabling and confusing those systems,when it is off the ground.

front or rear wheel drive ,as only ones i havew worked on are rear wheel drive ,so do you mean the half shaft seal

Sounds like there may be a problem with the left front wheel bearing/hub assembly easy to replace only takes about 30-45 min and about $55-125 in parts. Jack both front whels up and with it in drive turn wheels back and forth and listen to each side. I am pretty sure it is the left side but check both.

sounds like another bad hub brg, jack up front end and check for play in wheels from top to bottom wiggle for movement. A loose wheel brg will set a front speed sensor code.

there may be a software update for the powertrain control module for mis-fire monitor. check with your local dealer. but if thats not the case,these engines are known at least in my experience of having the heads crack between the valves and cause mild mis-fires. try compression testing all the cylinders and performing a leakdown test on them as well.

rear wheel drive