The idea that physics encourages "pursuing universal truths" is an ancient philosophical idea that was abandoned many time ago.
Yes, the general theory of relativity and quantum mechanics are incompatible, but this is not anything special; the history of science is full of cases where two or more incompatible theories co-exist until finally the incompatibility is solved by developing a new theory. Special relativity was born of the incompatibility between Maxwellian electrodynamics and Newtonian mechanics. This is one of the ways that science advances, the other way is when some new phenomena is detected that cannot be explained by existing theories.
Newtonian theory has not been refuted, simply its field of validity reduced.
"set the wheels in motion inside the minds of intellectuals who were
disturbed by the empirical confirmation of hypotheses based on false theories and one such genius was Kurt Gödel". The only intellectuals disturbed would be those that do not understand science. Theories as Newtonian theory are not false, they continue to work nicely within their margin of validity. because those 'hypotheses' continued being valid empirically. That is the reason why we continue teaching Newtonian physics in Schools and Universities.
"Even today, main stream physicists do not believe that what they discover is not universally valid". When a physicist proposes some fundamental principle, she or he does as a tentative hypothesis if there is no reason to doubt on the universality of the principle. If the next century new experimental data is found that disagrees with the principle then the region of validity of the principle is reduced, the new data is analyzed, and some new principle compatible with the new data is developed. Again there is no problem here with the standard scientific method way of work.
"Scientists, of course, know that chemistry is more fundamental than biology and physics is more fundamental than chemistry. Certain things can be derived from some other things and if something is derived from another, the latter is more fundamental than the former." Maybe for scientists that still believe on the older reductionism vision of science; the rest of scientists know that biology is not applied chemistry and that chemistry is not applied physics.
"A thing that is defined is defined in terms of things other than that thing. The crux of the matter is how well we can define things. For instance, we can define z in terms of a, b, c, d, etc. Symbolically, z = f(a, b, c, d, ...) if z can be defined in terms of a, b, c, d, etc. the next question is how we are going to define a, b, c, d, etc. It is clear that on the one hand if a, b, c, d, etc. are not well defined, it is not possible to claim that z is well defined. And on the other hand, a, b, c, d, etc. cannot be defined because if they are to be defined then they have to be defined in terms of other things such as a in terms of a1, a2, a3, a4, etc. and b in terms b1, b2, b3, b4, etc. and so on and so forth. This 'infinite alterity' might give rise to religious concepts such as divinity, etc. but what is clear is this unending sequence entailing definitions confirms that there is no thing that is well defined with sufficient rigor and clarity. It is clear that anything that remains undefined becomes latent assumptions and what is left over without being properly defined prevents building universally valid knowledge."
Any physical theory is constructed in terms of elementary concepts, not defined in terms of anything more fundamental and characterized only by formal properties laid down for them and in terms of derived concepts. The lack of definition for the elementary concepts do not invalidate the rigor with the which we can define the derived concepts.
You quote Born, but you don't give the whole quote, which is: "I am now convinced that theoretical physics is actually philosophy. It has revolutionized fundamental concepts, e.g., about space and time (relativity), about causality (quantum theory), and about substance and matter (atomistics). It has taught us new methods of thinking (complementarity), which are applicable far beyond physics."
He really means that modern physics was touching fields of knowledge previously restricted to philosophers. But this is not exclusive to modern physics, but just the history of science. Science has been always increasing its field of applicability and reducing the scope of philosophy.
Yes, Richard Feynman said that about philosophy of science, scientists, ornithology, and birds. He was absolutely correct. I am a scientist and philosophy of science has been totally useless to me, I would even say reading philosophical works have been totally counterintuitive because as Feynman stated "Philosophers are always on the outside making stupid remarks".