Strange

Sigh. There is no pushing and no acceleration. (I'm sure this has been explained many times already, and the PDF you attach explains it as well.) Much as I worry about encouraging your nonsense, you might want to read about the Gullstrand-Painlevé coordinates. These can be interpreted as space flowing towards a mass. https://en.wikipedia.org/wiki/Gullstrand–Painlevé_coordinates http://jila.colorado.edu/~ajsh/insidebh/waterfall.html It is idiotic to say that space-time doesn't exist. The Michelson Morley experiment (and others) disproved the existence of the luminiferous aether, not space.

And are these little anecdotes supposed to be relevant? Yes, you need to use general relativity.

Yes, gravity is a force in Newtonian gravity. In GR, it is slightly more subtle: gravity is a result of the curvature of space-time.

Well, you can't know that. It is one of those unfalsifiable ideas like solipsism or "the universe was created 15 minutes ago but just made to look as if it were billions of years old". You can't disprove this. Your gut instinct may be reassuring but is not evidence. And as we know that gut instinct is very often wrong, then I would not rely on it as proof of anything.

This is difficult to do directly because you have to bring the clocks together again at the end (and that introduces the complication in the second part of your question, below). The most obvious example is muon lifetime. http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html These are looking at the case where one person remains on Earth and the other goes away and then returns. The situation is not symmetrical in this case. There have been some excellent breakdowns of how this works in other threads (look, in particular, for posts by Janus. He/she explains it extremely clearly - far better than I could).

Perhaps because you can remember yesterday, and it was different from today?

Either can say they are stationary and the other is moving. Both can say the other is moving at 0.5c. Both will see the other's clock run slow (ageing less). And I wonder if this is the point of confusion: when speed is specified in terms of c, it is being described as a fraction of [the numerical value of] c not relative to light. You can't measure the speed of anything relative to light (because light is not a valid frame of reference).

You can only tell if you are moving relative to something else. So what is it about?

No, really. It makes no sense. If you can't understand the concept of division, I can't really help you.

I have no idea why you would think that. It makes no sense.

It is the fact that c is independent of the frame of reference that means it can be used as a way of defining speed.

All motion is relative. So you define the speed relative to something. Typically, you assume that your own frame of reference is "stationary" and measure speed relative to that. Or you might say choose some other reference. For example, if you want to calculate the path of a ball being thrown on a moving train, it may be simpler to use the train's frame of reference.

Tricky one this. It might involve some advanced concepts you are not familiar with. Say something is moving at 150 million metres per second. Then it is simple arithmetic to divide that by the speed of light to find it is (approximately) 0.5 c. Hope that helps.

So a tiny proportion of it warms the Earth (and provides almost every source of energy).

Sigh. Dark energy does not expand the universe. Come back when you have a mathematical model.

Perhaps because of his tedious attitude.

I somehow doubt that it was a per diem figure. Perhaps annually? Which would make it about 3 cents. Not completely implausible.

Only if it badly needs pruning because it is getting in that way of the experimental apparatus. (We have a general gardening thread.)

IF there is any such thing, then it may be psychological (like the way stroking a pet can reduce blood pressure). Bad science fiction can be so confusing.

It would be completely unusable, not just inaccurate.

Only worth considering by someone who has no idea how science works. Hundreds. Maybe, thousands if you count the tests if Lorentz invariance. http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html https://en.wikipedia.org/wiki/Tests_of_special_relativity https://scholar.google.co.uk/scholar?q=experimental+tests+of+special+relativity https://en.wikipedia.org/wiki/Modern_searches_for_Lorentz_violation Plus all the tests of general relativity. https://en.wikipedia.org/wiki/Tests_of_general_relativity Feel free to show that all of those have errors that precisely replicate the predictions of theory. https://scholar.google.co.uk/scholar?q=experimental+tests+of+general+relativity And here is a cheap experiment you can do yourself: https://www.forbes.com/sites/startswithabang/2017/04/27/how-to-prove-einsteins-relativity-for-less-than-100/

A few centimetres, currently. As the accuracy of measurements increases, this distance will decrease. Take the example of GPS satellites at an altitude of 20,000 km, in this case, you cannot just use velocity and the Lorentz transform to work out the difference in clock rates. You have to use GR. So SR is an approximation. When and where that approximation can be used depends on the accuracy of the measurements you need to make, and the environment you are making them in. Currently, the most accurate clocks we have can detect a difference in gravitational potential equivalent to a few centimetres of altitude.

There is no "distance range".

Because Lorentz Transforms are part of SPECIAL relativity that only applies locally in flat space. The expansion of space is described by GENERAL relativity. (How many times have you been told this, now?)