Dude, that's how science works. As a theory passes more tests, you gain more confidence that it is correct.
That's a misleading statement.
I can give an analogy. Do you know any calculus? Take the indefinite integral of x dx, you end up with the answer x2/2 + c. Without knowing the boundary conditions of the integral, you don't know what that constant c is.
There's a similar thing in GR . It has a term (called the Cosmological Constant) for which there's nothing in theory to determine what it is, and it is equivalent to a boundary condition - the overall energy density of the vacuum. It can only be set by observation. As a working choice, he took a value that made sense to him. It is NOT a prediction of GR - it was Einstein imposing his desire for a steady-state universe on his solution. But eventually observation revealed that the universe wasn't steady state, and we accepted new estimates for the constant.
Note that it is a cosmological constant. Not a local constant. It isn't relevant for short length scales (like, a couple hundred yards across an Alcubierre drive spaceship).
Not really. Not in the way you implied here.
Einstein published general relativity (in 1915). Within a matter of days1 of receiving a copy, Karl Schwarzschild, colleague and friend of Einstein, wrote back detailing a solution2 to the equations. Schwarzschild had worked out the shape of spacetime around a massive spherical object, like a planet or a star. And, in that solution is it bleedingly obvious that for a massive enough object, you get a singularity.
Einstein liked Schwartzschild's work. As I recall, he didn't have any objection to the idea of "frozen stars" as they were called at the time. However, others were not so sanguine. Arthur Eddington famously said, “There should be a law of nature to prevent a star from behaving in this absurd way.”
And, they set out trying to find reasons why a frozen star couldn't form, or a flaw in Einstein's General Relativity that would keep this from happening. It was rather like people trying to poke holes in the math of the Alcubierre drive, honestly. Thing is, they were all incorrect. No changes to GR were required.
This is how science works. Attempts to disprove a thing, or poke holes in it, are tests. The forumulation of Einstein's general Relativity has been tested many times over - from detection of precession of Mercury's orbit, to discovery of gravitational lensing, to the radiation coming off Cygnus-X1 (the observatin of a black hole), to detection of gravitational waves. No changes to the overall formulation have been required. There are some things predicted by GR that can't be tested yet, but everything it has predicted that we can test, turns out to be correct. It is stunning in this regard, but true.
The outlying issue is quantum mechanics, which is incredibly difficult to match up with Relativity. But, we have yet to figure out what changes, exactly, this may require in GR, if any. It may be QM that needs adjustment.
1. Which was remarkable, because in December 1915, Schwartzschild was literally in a trench fighting WWI.
2. In this context, "solution," means, "application to a particular scenario". Einstein's equations are general, like saying y = mx +b. You need to apply it to a particular situation to say what m and b are, and then you can give a Y for any X you like. Einstein's original paper was the construction of the general form, and did not include applications to particular scenarios.
