Speed of an object (moon, planet, star, starship) accounts for an increase in mass... so in a sense gravity is greater for the same object being at rest... but... The curvature of space-time (gravity) is the effect of mass ... You can have a 'static' object still exerting Gravitic forces...
As to your second point I could suggest that space expanding from all sides (4d space time) it would nullify it. Outside galaxy space expanding would cancel out the potential of clusters on the MW fringe from getting out of the spiral fringes. As a star creates a 'dimple' of curvature in space...
You can consider the "small universal constant" (notion that has been revived through mathematical calculation by Hawking) as being the effect of space expanding...
The Doppler effect is based on 'distance and speed' (simple terms) The space expanding would account for both distance and speed ... A race car on the track ... the track is expanding and the car sits still ... u still observe a Doppler effect as the distance increases... from your own point of...
There are several scientists (including Stephen Hawking) who made calculations about our Galaxy rotation and mass... The only stable Milky Way construct they were able to come up with had to include in it's calculation the so called "Dark Matter" ... As I am a realist I just can take seriously...
This was meant for the top POST
:blushing: The math that you worked out, I think that it can not be validated at the quantum level... especially in describing the spin proprieties of fermions...
I am not a pro but I also think that being that the arrow of time does not change it implies that...