Hubble's law and postulates of Big Bang says that all the Galaxies are moving away from us. The general mapping of universe around us (barring the Milky Way Obstruction area) also confirms that our universe is Isotropic and Homogeneous, it is also well settled that we occupy no special place in the Universe.
Our Galaxy is moving with reference to some Extra Galactic Reference at a speed of around 600 Km / Sec, based on Hubble Law and Red shift observed we have concluded that a few distant Galaxies are moving away from us at a speed of around 30000 Km/Sec.
Since our Universe is Isotropic and Homogeneous, so it does not matter if we are observing from Earth or from any point on any other Galaxy which is moving away at a speed of 30000 Km/Sec from us. Since we are moving at a speed of 600 Km/ sec, the least speed of this Galaxy would be around 29400 Km/Sec. Now if we put an observer somewhere on this Galaxy, then also we will see the same kind of isotropic and Homo map of galaxies and stars around it. So…
a. Applicability of Hubble's law will soon make a Galaxy run away at a speed of light. That’s some speed for such a huge mass. Here comes Gravity Red Shift?
Note: All my answers will relate to interpretations of the Big Bang model, which is not necessarily a testament to the model's validity.
Galactic redshifts are a correlation of galactic redshifts to distances. The Hubble formula was derived from Special Relativity and relative motion. According to the Big Bang model (BB) space is expanding. We cannot observe this at stellar scales, not even at galactic scales concerning out Local Group or maybe even our local galaxy cluster Virgo. We have to go to super-cluster distances to observe galactic redshifts without major relative motion.
As to your question, there is no real motion involved with the concept of expanding space, so velocity is not involved.
b. We would be a very remote Galaxy for this shifted observer, so how come we are traveling at a very low speed (leave aside the relative aspect). This observation indicates that there got be some special place.
Again, there is no speed or velocity involved according to the hypothesis of expanding space.
c. There are few blue shifted Galaxies also, including our Andromeda, wherein we expect to collide in next 4 b years? Why ? The explanation is that they are all in local groups and have some peculiar velocity. Universe is Homogeneous and Isotropic, so why this peculiar velocities for our Local Group. Even some of very far Galaxy or cloud systems are giving blue shift that directly violates Hubble law.
This is a very common misconception. There are over 7,000 blue shifted galaxies and counting, most are only very slightly blueshifted. All are thought to be within the local Group and supercluster Virgo and all are thought to involve relative motion as being the cause of blueshifting.
http://fittedplane.blogspot.com/2009/12/blue-shifted-galaxies-there-are-more.html
d. The balloon analogy of space expansion does not explain this vast difference in the speed of Galaxies, moreover if the space itself is expanding, then how can we collide with Andromeda in 4b years, fine there must be some Gravitational pull between the two, but was it present from the day these Galaxies were born, because new pull can only become effective if the rate of amassing the peripheral mass is much faster then the rate of space expansion.
e. Why there is a total absence of expansion of inside of Galaxy or Solar System. A dot on the baloon surface expands with its skin. An expansion which can cause huge speeds for Galaxies, cannot per say disturb the internal arrangement ? It is also not the case that Gravitational pull of constituents is a very strong force?
At very close distances such as within our galaxy and our closest large galaxy Andromeda, the expansion of space is not observable.
f. Why is that our Solar System which has passed many a times (around 20?) through the Density Wave Arms region of our Galaxy, and still surviving with its planets? Density wave region is supposed to be great breeding place for new stars, obviously its not a smooth high speed expressway for our solar system? Or we can say that it ducks or jumps this region and gets out of the plane and moves either up or down?
The density wave hypothesis is presently entirely dependent on the dark matter hypothesis, both of which are hypothetical since there is no direct evidence for their existence.
g. How can a Galaxy maintain its basic structure with an observation that the orbital speeds of all the stars is almost same (leave aside near to center stars)? The closer stars will move faster angular-ly leaving behind the distant stars, thus changing the basic structure of the Galaxy. So the shape we see today of our galaxy (in photo of course), is it the same when our Sun was born (around 4b years ago)? The point is what are we seeing in the photo (the present or may be few billion years ago shape?)
The Big Bang model has a number of different hypothesis to explain your question but no consensus explanation that I know of.
h. Gravitational lensing is a great observation, great analysis. My only question is if you bend the light angular-ly, that means some deceleration has taken place. How does it justify the constancy of light? I can tell you fall below c and Energy is no longer Energy, it becomes Mass+Energy, and then the poor combo cannot make it to Earth.
The aspect of the speed of light (SOL) that most students don't understand is that the SOL is a ratio of distance traveled per unit of time. As the distance travels decreases so does the rate of time which maintains the constant ration and the SOL.
i. Inflation is supposed to be microscopic expansion from a singular particle of infinite density with a faster than light speed. Relativity is violated even after t = 0?
j. And by the way if it was faster than light, why no traces of anything moving at faster than light (even if we take relative speeds can we get more than 2c?)
Inflation is also a group of hypotheses that proposes physics unique to the hypotheses themselves. Faster than the SOL is a requirement of these hypothesis and the ending of the Inflation period is also part of the numerous related hypothesis.