It is true that the strength of a gravitational field affects measurements of space and time. However, except at discrete points occupied by black holes, and perhaps other extreme objects if one is very close to a surface, our location is in a 'weak field situation' as is most of the Universe. We are not in a region where the suggested biases could play a role.
The 'filamentary' and 'bubbly' structure of normal matter has been detected within the relatively 'small' distance of a few billion light years. The scale of the filaments and bubbles/voids is such that, the relative motions of the galaxies which define those structures are too small to have significantly altered the structure during the equivalent few billion years.
Yes, most spiral galaxies that have been studied appropriately do not follow a Keplerian velocity distribution in their outer regions. That is, rather than the rotational velocity decreasing with increasing distance from the galaxy's centre (as the orbital speeds of planets decrease with increasing distance from the Sun) the velocities either remain roughly constant or, in some cases, increase with distance from the centre of the galaxy. The usual explaination is that there is a large halo of dark matter.
There do seem to be massive black holes at the centres of most galaxies, but they are very much smaller than what we call the 'core'. Relativistic effects will be signifivant very close to those nuclear black holes but very insignificant throughout the much greater volume of a typical core. The cores of galaxies constitute 'weak field' regions.
4.The Big Bang
Yes, the Big Bang event does define a zero point in time ... cosmic time.
Special Relativity says that a clock in one inertial reference frame runs 'slowly' as measured with respect to a clock in another inertial reference frame. A full discussion leads one into a consideration of the meaning of 'simulaneity', etc.
We are not observing the 'cosmic clock' from another reference frame, i.e. from outside the Universe. The 'clocks' and the measurement of their rates are fundamentally different in those two situations. We are integral components of the cosmic structure that is evolving in step with the 'ticks' on the cosmic clock which began to 'tick' 13**9 years ago, just as my 'ticking heart clock' began at a well-defined time as measured by clocks in my local not-relativistically-affected corner of the Universe.
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