Orbiting around a black hole Is it possible (for either a satellite or a planet) to orbit around a black hole? Do they attract everything around themselves into the center? Or they just affect gravitational force just like stars?
Absolutely possible. There's nothing magical about a black hole. The gravitational pull of a black hole reaches as far as gravity would for another object of the same mass.

If you replace the Sun with a black hole of the same mass, everything would continue to orbit it just as it currently does.

Anything with mass has a gravitational force itself, and a black hole will attract anything with mass. Again, it's the same as our star having an effect on the Earth, and the Earth having an effect on the Moon.