What may be the period and speed of revolution of the star that is closes to galactic centre?
Star S2 reaches maximum velocities of 5,000 km/s according to this ESO page.

The orbital period is given as a little over 15 years and this paper gives a peri-center (closest approach to the black hole) of 17 light hours.

There's another star in the area called S0-102 which has a shorter period, but its orbit is less eccentric - so its closest approach to the black hole is further out at 36 light hours. Its maximum velocity will probably be less than S2 but I haven't been able to find a figure.