What is something you can see in outer space from opposite sides of the earth at the same time? i.e star

If by opposite side of Earth, you mean the north and south poles, hypothetically a star on the celestial equator would be visible to both observers, assuming both have clear horizons and are some altitude above sea level. In all pracitcality, this won't happen. If the Moon or Sun happen to have a declination of zero degrees, either of them could straddle the horizon for both observers.

If by opposite side of the Earth, you mean 180 degrees of longitude apart, and both are on the equator, both observers could see a star at either celestial pole, again, assuming high enough elevation and a clear horizon. However, there are no naked eye stars at exactly 90 degrees north or south declination. I believe the answer you are supposed to give is either "nothing" or Polaris, which is about one degree away from the NCP.

The Sun can be seen by observers positioned at sunrise and sunset points at the same time.

At the Full Moon phase these observers could also see the Moon rising or setting during sunrise and sunset points.

Because of the Earth's axis tilt, at the seasonal solstices observers on the equator, on opposite side of the Earth, can see the Celestial Pole regions of the sky over the hemisphere experiencing the winter season.

Any object on a horizon, like the eastern horizon for one, western horizon for the other, or the northern horizon for a person at South Pole, and southern horizon for a person at the North Pole.
Moon, sun, a star or a planet would qualify

Nothing. Unless you take relativity into account, and even then it's only theoretical.

You can not see any one of the stars from opposite sides of the Earth-at the same time.

Comet tails and the Milky Way galaxy.