Understanding expansion of the universe I'm having problems to understand "graphically" what is the expansion of the universe.
Does it mean that if now we have two points A and B separated by 1 meter, in a future those points will be separated by 2 meters, even without any force or movement between them? just because the space between them was expanded?
 A: The universe is expanding, but the moon won't get any further from the earth. Gravitationally (or electromagnetically or strongly or weakly) bound systems are exempt, if they are sufficiently bound. I think this passage explains it well. (Source)
The reason for this is subtle, and is related to the fact that the expansion itself isn't a force, but rather a rate. Space is really still expanding on all scales, but the expansion only affects things cumulatively. There's a certain speed that space will expand at between any two points, but if that speed is less than the escape velocity between those two objects -- if there's a force binding them -- there's no increase in the distance between them. And if there's no increase in distance, that impetus to expand has no effect. At any instant, it's more than counteracted, and so it never gets the additive effect that shows up between the unbound objects. As a result, stable, bound objects can survive unchanged for eternity in an expanding Universe.
A: this is not correct, 1 meter distance will always stay 1 meter, when we say the universe is expanding it means all galaxy clusters receding from each other because of Hubble constant, however, the Hubble constant itself is too tiny to see its effect in our solar system.
if the space expanded everywhere we would see rotational speed up of compact objects, which we do not observe
A: So, let's get some perspective. The figure I got for the rate of expansion is 68 kilometers per second per megaparsec. 
68 x 10^3 / 3 × 10^19 = 2.3 x 10^-17 metres per second. 
I make that approximately 4.3 x 10^9 years to expand by 1 metre! A billion years! That's a bit more that 4 metres over the age of the Earth. 
What non-cosmological effect is going to show that? Electromagnetic and even gravitational energies will counteract this very slow stretching with only minor adjustments. 
Except, that the expansion is accelerating, so one day the ratio will change, and we have this to look forward to https://en.m.wikipedia.org/wiki/Big_Rip
