English is preferable, i might be making some spelling mistakes, and i apologize for them, but the technical terms are all english, i hate to try and find translations...

first about the hubble "constant" changing -
the constant is constant in space, but not in time.
now, i'm about to step into a subject i'm no expert about, i apologize for any mistakes i might make -
the way to build a metric one can work with to describe the universe, in a GR way, is to "slice" it to equal-time three dimensional "planes".
the simplest way is to assume that the universe is euclidean at short ranges (observations of near space confirm that, near meaning as far as we can see, if i'm not mistaken), and then define a metric from a point of view of a "all-knowing" observer, that is one that can measure distances on the plane, between any two points.
now, for every two points on said metric, in every plane, the same hubble law holds, that is - the velocity between the two is proportional to a constant that is the same one in all space at that time.
the relation between said constant and the expansion rate of the universe is H(t) = a*/a (with a* being the time derivative of a, a "dot") where a is the expansion factor of the universe (has to be normalized to some a_0 if u want it to mean anything).

as for measuring galaxies at different times, i think that compensation can be done.
one way is to measure "near" galaxies, where time differences are small in cosmological orders of magnitude.
another, i believe, is measuring relative velocities of objects about on a line of sight (seems tricky to me, i don't know if it's actually done).
this is an interesting point, i think i've heard an answer to it once, and am sure i've asked it once, which make my not knowing it now somewhat dissapointing (and depressing, considering the implication about my memory), so i will check with my sources for the answer, and be back.

an important point, i think, is that predicitons can be made, according to the standard model, regarding what the hubble expansion should look like, if the modle's assumptions and derivations are correct, including "looking into the past" effects, and as far as i know the observations match those to a good degree.

be back with more precise answers soon, i hope