I am trying to understand the wobble.
So the car wobbles a bit in 2nd, 3rd and 4th gear from 3k to 5k. So the car wobbles nearly continuously from 30 km/h to about 90 km/h. This happens in all road condition not just on a stretch of uneven road. Is the wobble the same when going down hill?

I think your observation in turning the wheels by hand is OK as the steering wheel/rack is on the right side.

Have you asked the opinion of a car mechanic?