Going over bumps or bump roads, stearing shakes,pulls, at any speed fine after 15 min park

sounds like strut bearings did not get replaced

Can you provide more info? Did you hit a bump? What do you mean by 'drives bumpy?' Does it ride rough, or does it go up and down a lot after you hit a bump, or something else? Can you further describe the snap you heard, and what was going on when you heard it and immediately afterward (e.g., driving 40 mph on a paved road, hit a pot hole, heard a loud 'breaking' sound as if something snapped/broke, and the ride of the car seemed to immediately change to being more harsh/rough)? Have you had any work done recently, such as tires changed or rotated, struts replaced, wheel alignment, or brakes replaced? Did anything else change (e.g., now when you hit a bump, you hear a new noise in the rear)? Were you carrying anything heavy in the trunk or back seat? I had a '99 Corolla for several years, and had zero problems other than a worn out driver's door handle and a couple of cracked windshields. Great car choice!

wheel bearing is the first to be check. lift the car on the lift and push/pull the wheels in and out. if excessive play replace the bearings.

the caster needs to be checked as well as loose steering components too much negative caster will cause this also too much air in the tires

Yes there is and it will be in ya stearing colum. Chance are it is a wire that has chafed though. Pull it apart and inspect all your wires it could only be a small hole in one wire causing the problem.

I recommend having the stuts and stabalizer bar and swaybar links looked at to make sure they aren't worn

It isn't the power steering box. You have some worn or broken components in your front end. I would only drive it to a garage to get it onto a lift.

its probably your bump stops. the vw ones are very soft. i bought ford escort (the shape after the xr3) ones and cut them a little down to fit. i think the noise is either your shock touching or the sound of the tire scraping the body of the car. hope this helps.

is this noise coming from the front or back?

have you had a front end alignment