Presumably, Einstein brought these ideas to the world first.
Actually, the idea of spacetime, or at least spacetime as the “geometric” formulation of special relativity was not formulated by Einstein, but by his former professor, Hermann Minkowski. Einstein initially disliked the spacetime formulation, calling it “superfluous learnedness”, before utilizing it in his theory of general relativity, which allows spacetime to curve under the presence of mass-energy and “causes” gravity.
Answering this question is a bit difficult because it needs to be a bit more specific. If you’re talking about spacetime in the context of special relativity/general relativity, then you’re talking about a spacetime whose metric (essentially a general form/correction for the pythagorean theorem in curved or flat space) has a signature such as $+,-,-,-$ or $-,+,+,+$. This means you write a new “pythagorean theorem” in say, Minkowski (Flat) Spacetime as $$ds^2= -c^2dt^2+dx^2+dy^2+dz^2$$ or $$ds^2= c^2dt^2-dx^2-dy^2-dz^2$$
The choice of coordinate system is also arbitrary. The $c^2$ factor is also just to get equal units for space and time.
This metric preserves the speed of light in all reference frames, meaning the speed of light is invariant for all observers. No matter how fast you’re moving or how fast the source of the light is moving, seemingly paradoxically, the light will always appear to move at the same speed, at about $3*10^8 m/s$.
So really, your second statement includes the first. So I guess logically I’d have to say the spacetime idea, since it’s also used wildly in different theories in physics, obviously general relativity being one of them but also quantum field theory and encompasses the first idea.
As for which shocks physicists the most, I can’t really say for sure since I wasn’t alive when this was discovered, but I imagine, philosophers had already considered for a while the melding of space time into one thing, but the speed of light appearing the same for everyone is so seemingly paradoxical; I imagine it would be more surprising. Like if you throw a ball forward in a moving car, you’d expect the ball to be moving at the speed of the car plus the speed at which you threw it, right? Well, change the ball to a ray of light. Now no matter how fast the car moves, the speed of the ray is always the speed of light, it never changes. That’s weird as hell.
As for if these ideas are “done deals”, I don’t think they are, since nothing in science is set in stone, but they are so well-supported that at this time there is no reason to doubt them. It’s worth noting thought that some quantum “theories” of gravity predict tiny deviations from special relativity, which i believe affects the speed of light a little. I believe this comes from Loop Quantum Gravity, where the spacetime structure itself is different. So like I said, the spacetime background itself affects the speed of light, so the two questions are pretty linked. It’s important to keep in mind though that no deviations from special relativity have yet been observed.