No. The sun orbits the center of the galaxy, not any star. Alpha Centauri just happens to be the nearest star system to our own.
"Alpha Centauri", or "Toliman", is not a single star - it's a system of three stars.
Alpha Centari is the nearest star to the Solar System's Sun. Alpha Centari is thought to be in the order of at least 4 to 7 billion years old. The Sun's age is estimated to be at the low end 4.6, and thus likely to be much younger. Another difference is that Alpha Centari is really a binary star system, while the Sun is the only star in the Solar System.
Alpha Centari is the nearest star to Sol. It is about 4 light years or 24 trillion miles away.
Alpha Centauri AB is a binary star system. It is 4.37 light years away from our Sun. Both Alpha Centauri A and Alpha Centauri B are in close orbit around each other, so the same distance is valid for both.
As of current knowledge, there are no known satellites orbiting Alpha Centauri, which is our closest neighboring star system. However, further exploration may potentially discover any satellites that might exist.
Arcturus is the name of a star - also known as Alpha Bootes.
A star and all the bodies that orbit it is called a, "Star System". The star system that we live in has been named . . . we call it the Solar System, because the name of our star (The Sun) is "Sol".
None are known yet. Some evidence suggests that a small planet may be in a close orbit around Alpha Centauri B, the second largest of the three stars in the system.
Proxima Centauri, at about 4 light years, is the closest star after the Sun, followed immediately by the binary stars Alpha Centauri A and B. Proxima Centauri is thought to orbit the Alpha Centauri system in an extremely wide orbit. Theoretically there could be some as-yet-undiscovered small red dwarf or brown dwarf closer to the Sun than Proxima Centauri.
Menkar (Alpha Ceti) is the alpha star in Cetus.
There is no star that is simply called "Alpha". There are several that have "alpha" in their name, for example Alpha Centauri, Alpha Cruxis, Alpha Canis Majoris, etc. - usually the brightest star in each constellation. Some stars such as Betelgeuse (Alpha Orionis) are not actually the brightest star in the constellation.
There are no stars that I am aware of named "SMN". The nearest star to Earth is Proxima Centauri, and the next-closest stars are the binary pair Alpha Centauri and Beta Centauri.