The "Science" of Physics was "settled" back in the time of Issac Newton. Oops, then came Einstein along!
Well, yes and no. Yes in relativistic environments (near light speed) you get a different physics. But this is only applicable to elementary particles and the like.
You were doing ok until the `but'. Relativity applies to everything (matter + energy) in the universe, not just elementary particles. If you were able to move close to the speed of light, you'd see the weird effects of SR. If you were traveling near a massive object, you'd see the effects of GR. You see relativistic effects in measurements made.
For the rest: all the calculations that were done previously using Newton's laws: the force needed to change the speed of an (not relativistic) object (cars, trains, elements of a machine...) are STILL calculated using newtons law.
Because 1) it's way easier and 2) the error isn't large for slow moving (relative to c) objects or objects far away from other massive objects.
I can assure you that whatever new theories there will be found concerning the laws of physics they will have to comply with all known observations and therefore will have to be in compliance with newton's laws for normal day to day objects.
Yes. And that's what gave Einstein his fame. He was able to explain the problems physicist knew about with E&M waves moving at a constant velocity and the precession of Mercury and so on. in the proper limits, relativity reproduces Newtonian mechanics.
BTW talking about Bohr and the theory of quantum mechanics: there is no sane way to apply these to macroscopic objects. For that you NEED newton's laws. So in that sense they are more complementary.
Not quite. Quantum and Newtonian are not complementary. The same rules about relativity reproducing Newtonian effects also apply to quantum. That is, in the limit of large quantum numbers, quantum mechanics is to reproduce Newtonian mechanics (see: Correspondence principle).