There is a lot of approximations in your understanding of special and general relativity theories.

First, special relativity does not care about the distance between 2 observers. It doesn't matter as to how they observe the same physical phenomenon. However it is true that they will observe time dilation/contraction when their relative speed is high.
Your example of the laser beam will result in the two observers seeing the same light beam with a different wavelength. But they will measure the speed of a photon in that beam with the exact same value.

With regards to the general relativity, the theory says that gravity should be perceived more as a curvature of spacetime rather a force pulling things in a certain direction. In that regard gravity is different than electromagnetic forces. In general relativity the apple follows the shortest path to the ground in curved space. The same goes for satellites orbiting the earth. This has been finely observed many times and is today practically used with GPS technology where Newtonian predictions would yield to large positional errors quickly.

It's all fine to doubt well established theories and general relativity may well be replaced by a more precise theory. But in order to do this you need to present scientific arguments, including measurements, that validate the new proposal.

Questioning established theories is a good thing though.