Yes, it means both. To go up the stairs and down the stairs. Ex. I took the stairs down to the lobby. I took the stairs up to my room. How did you get here? I took the stairs.

Yes, it can mean either up or down the stairs.

It can mean either to go up the stairs OR to go down the stairs. One way or both.

Yes, you would use those, depends on which direction. If you want to go from low to high, you would say "I went UP the stairs." If you want to go from high to low, you would say "I went DOWN the stairs." Hope that helps/ Or you could just say I took the stairs, but you should make it clear where you started and where you are going.