Yes, of course. The space between us and the sun is nearly a vacuum, yet we experience its gravity -- it keeps the earth "on track," AND it contributes about 1/3 of the motion of the tide (the other 2/3 being lunar in origin).
Gravity is not affected by vacuum. every particle of matter in the universe, including dark matter, pulls on every other particle. The force of gravity (which according to Einstein doesn't exist) obeys the inverse square law so gets rapidly weaker at a distance. If two astronauts did a space walk and stayed still long enough relative to each other,they would drift together because of their individual gravitational attractions
Yes. More to the point, gravitational effect *only* depends on the affected masses, and not on how much or how little gas molecules are in between.
Sound depends on molecules for transmission, and in space, the speed of sound is "zero". But the effect of gravity is not attenuated by more or less gas.
In a vacuum, gravity causes all objects to fall at the same rate. The mass of the object does not matter. If a person drops a hammer and a feather, air will make the feather fall more slowly. But if there were no air, they would fall at the same acceleration.