How do we know gravity attracts in all directions at once?
Because my daughter in Australia tells me her pencil falls down, not up.
Mass appears to attract other mass, irrespective of position or orientation. That is, gravity is attractive no matter what.
Yes it is. Note that a concentration of energy causes gravity, not just mass. It's usually in the guise of a massive star, but it's the E=mc² energy content that causes the gravity. And then a passing light beam curves towards the star, not away from it. See Ned Wright's deflection and delay article:
In similar vein matter falls down towards the star. IMHO to understand this all you need to do is think of pair production and the wave nature of matter.
Contrast that with electrostatic forces which could attract or repel depending on the charges involved, or a voltage between two metal plates which has a specifically directional force on electrons travelling through it.
Electromagnetism doesn't work the same. The electron has a "spinor" nature, and the positron has the opposite chirality.
How do we know gravity attracts in all directions at once? What experiments have been done to confirm this?
When you go to Australia, you don't fall off the bottom of the world!