True. Add in the fact that you are seeing back in time (8.3 minutes in the case of the Sun) and you have got it.
Two possibly complicating factors here: one is the problem at sunrise and and sunset, when the motion of the earth is parallel or antiparallel to the direction of the light, this divergence is minimized. Also, the earth is not a sphere, it is an oblate ellipsoid (i.e. a beachball with an elephant sitting on it, not a football).
Correct again.
Also, you have the issue of what the ancients called "lack of stellar parallax" -- the distance between the stars and the earth is so great, one can travel anywhere one likes on Earth without affecting the apparent relative positions of the stars. I'm just a little too tired to decide if something analagous would kick in here.
Correct again. The distances are so far that Triangulation doesn't work. Remember that we are also looking into the past and that in some instances (Hubble) we are looking billions and billions of years into the past, at objects that no longer exist.
Define this term, please, or provide a link.
For the record, I seem to recall that we have the earth orbiting the Sun (close enough for govt. work, anyway, given the ratio of the two masses; and we can consider the effects of the moon and other planets as mere perturbations), in addtion to rotation of the earth about its own axis -- which is not perpendicular to the plane of its orbit about the sun.
To say that "the sun is also orbiting the earth" is misleading: this is not a two-body system of equivalent masses, the error introduced by treating the Sun as the center of mass is very small.
I think LG is confusion the aberration of light issue with the (approximate) two-body problem.
Cheers!