Is there a black hole in the centre of the Milky Way? Is it true that the whole galaxy is actually revolving, and powered by a black hole?
Has it been proven, and if it is true, how can our solar systems actually keep up the momentum to withstand the pull?
 A: I think the other responders adequately covered the "revolving around" part of the question and made the point that the mass of the black hole is insignificant compared to the mass of the galaxy as a whole.  I just wanted to point out that, despite that, it appears that the massive black holes at the centers of galaxies like our own do have some effect on their host galaxies. Astronomers have observed a strong (for astronomy) correlation between the mass of the central black holes and the mass of the host galaxy. Bigger galaxies have proportionally bigger black holes. We don't really know why, it may have to do with how radiation produced as the black hole consumes matter influences the flow of material into the galaxy.  
A: Clearly as all the above comments have stated, in the overall scheme of things its a tiny fraction of the overall mass of the galactic system. I wouldn't consider thats its main effect to be direct gravitation however. Supermassive black holes may roughly control the amount of gas in their surrounding galactic cores. As the gas density nearby gets higher, the BH feeds on some of it, and shines as a quasar. All that radiation tends to push the gas away. So there is a case to be made that supermassive black holes may regulate the amount of gas and young stars in the core regions of their galaxies. But they do this because of the vast energy radiating from their acretion disks when they actively feed. The issue is not so clearcut however, as regions of active star formation create massive stars whose stellar winds (and supernova explosions when they die) have much the same efect. Supermassive star clusters such as the Arches cluster which is close to the Milkyways blackhole probably formed there because of the graviational interaction of the gas and the BH.
A: A black hole at the center of the Milky Way is an observation that is dependent on the validity of the general theory of relativity (GR). An input into an equation of GR is one of the steps to determine the existence of a black hole (anywhere). If GR is invalid, no black hole may exist there. No black hole has been directly observed. For confirmation of this see the Chandra X-ray Observatory FAQ.
A: The best evidence for the black hole at the center of the Milky Way comes from the simple Keplerian motion of nearby stars. 
Using orbital data deduced by scientists, I made a simulation of their motion. Please note that this simulation needs a browser that supports WebGL.
A: I was giving a talk about the galactic black hole at the center, Sagittarius A*, back in 1998. At that time, it was already clear to enlightened people that it had to be a black hole. An analysis of a two-temperature plasma helped to bring some new evidence that the object had a real event horizon.
The black hole is huge but it is not "galactically" huge. Its mass is 4.2 million solar masses or so. This is of course large, in comparison with any star, but it is negligible if compared to - thousands of times smaller than - the mass of the Milky Way.
So it would be unreasonable to say that the black hole has a tremendous impact on the gravitational forces across the Milky Way. It is just a heavy single object but if one looks at the size of 5% of the Galaxy's diameter, the total amount of stars in such a region is already vastly larger than the mass of the black hole. Already in such small regions, the black hole is just a small droplet.
Black holes, just like any other heavy objects, are unable to "power" galaxies. Galaxies are composed of stars that move according to the laws of mechanics (or general relativity) - inertia modified by the gravitational force. (Today, we believe that most of the gravitational force is exerted by the dark matter that represents a majority of the galactic masses.) The dependence of the gravitational force on the distance from the center of the Galaxy determines the orbital velocity of the stars at every distance. 
For every distribution of matter, we get some dependence of the gravitational force on the distance, and we can write down the velocities as a function of the distance for which the orbits remain circular. (And if the orbits are a bit elliptic, there is no problem with that, either.) Whatever the radial attractive force is, there always exists a velocity such that the gravitational attractive force exactly cancels against the centrifugal force. (More precisely, the gravitational force is the centripetal force.) So for any pull, there is a velocity such that one can withstand the pull, and it makes absolutely no difference whether a black hole contributes to the pull.
So while the object is interesting - and probably generic for most galaxies - it doesn't have any "systemic" importance for the functioning of the Galaxy. The radius of the object is millions of kilometers - something like 10 times the distance to the Moon. The matter around the black hole is being heated and "cooked" by the gravitational field and there's a high temperature. But if one managed to cross the event horizon, he could live for a few more seconds before he would be squeezed by the singularity at the black hole center.
A: There's a strong consensus among astrophysicists that there is a supermassive black hole at the center of our Galaxy (as there are in most large galaxies, apparently).  But as cool as that fact is, it's possible to make too much of it.  The black hole at the center of our Galaxy has a mass of a few million times that of the Sun, which is a tiny fraction of the mass of the whole Galaxy.  An object like the Sun, for instance, is attracted gravitationally toward the center of the Galaxy, but the black hole is responsible for only a tiny fraction of that attraction.  All of the other stuff is much more important.
One common misconception out there about black holes is that they "suck everything in."  A black hole of a certain mass is no better at pulling in a distant object than any other object of the same mass.  So if you weren't worried about the Solar System being sucked in toward the center of the Galaxy before you knew about the black hole, you shouldn't be any more worried about it afterwards.
A bit of self-promotion here: There's a bunch of stuff written about how to think about black holes, including Frequently Asked Questions about Black Holes, which I wrote back in the 1990s.  You can find it here: http://cosmology.berkeley.edu/Education/BHfaq.html
A: NO, at least by 3 reasons :
recently,as 2003, it was found that 40% of the matter in the vicinity (accretion disk) of the BH will be radiated away.   


*

*I'm convinced that all the matter, in excess above the limit, will be radiated away before a BH can be formed.  


quoting from WP-Black-Hole 

In the case of compact objects such as white dwarfs, neutron stars,
  and black holes, the gas in the inner regions becomes so hot that it
  will emit vast amounts of radiation (mainly X-rays), which may be
  detected by telescopes. This process of accretion is one of the most
  efficient energy-producing processes known; up to 40% of the rest
  mass of the accreted material can be emitted in radiation.[95] (In
  nuclear fusion only about 0.7% of the rest mass will be emitted as
  energy.) In many cases, accretion discs are accompanied by
  relativistic jets emitted along the poles, which carry away much of
  the energy. The mechanism for the creation of these jets is
  currently not well understood.



*The SMBH is a tentative explanation of the velocity/radius curve of the disk galaxies as if only a central force could explain it.
BUT: 'The galaxie's lopsidedness' (google it) to find that +-30% of the galaxies configuration can not be explained by a central force (which is axis symmetric).  

*The galactic field of a disk galaxy is best described by a vortex field instead of a central force one. ( google for images of hurricanes and for disk galaxies ) 
In this answer I'm not saying why the disk galaxies have such profile (vortex) nor why an enormous amount of radiation and accelerated matter that is swirling at the central region of the galaxy (a plasma by Lubos words) .
To the question I have to answer: NO.    
