Except during a lunar eclipse, when Earth's shadow eclipses the moon.
I guess that means the sun is on the opposite side of Earth and thus Earth is a globe.
Hypothetically you could have a perfect alignment of planets such that Earth lies directly on the path from the sun to another planet, but it would be too far away to be in Earth's umbra, so you would only get a partial eclipse with the Earth only obscuring a tiny portion of the light from the sun.
Its effect would be similar to a transit of Venus or Mercury. Earth would obscure a tiny portion of the sun.
For example, at Mars, the closest planet to Earth where this could happen, completely ignoring any issues of alignment and instead just having Earth at aphelion and Mars at perihelion and pretending they align, Mars would be 206.7 Gm from the sun, while Earth would be 152.1 Gm, making the distance between them 54.6 Gm.
Earth, with a generous overestimate of the radius of 6400 km, would have an angular size of roughly 48 arcseconds.
The Sun, with a underestimate of its radius of 695 Gm, would have an angular size of roughly 23 arc minutes, or 1387 arc seconds.
This means Earth would cover approximately 0.12% of the sun as seen from Mars. This would correspond to a tiny lowering of the brightness. Not anything you are likely to notice.
As for the stars, the stars produce their own light. They (other than the sun) are not illuminated by the sun, and as such you wouldn't expect them to be eclipsed by Earth, other than when Earth is literally getting in the way of your line of sight to them.
For the sun, we call this night.