It is a plane.
Geometric space is three dimensional and infinitely large.
In our real world, the space is 3D. It is currently unknown whether it is infinitely large.
Lines in Euclidean space.
Yes, unless specifically described as bounded.
Because the universe is neither infinitely large nor infinitely old. If you need more details, look up "Olbers' paradox".
Because the universe is neither infinitely large nor infinitely old. If you need more details, look up "Olbers' paradox".
Yes, a set can be infinitely large. For instance, the set of all odd integers is infinitely large.
The set of Pythagorean triple is three dimensional and infinitely large.
It's not really clear what you are asking, but in fact there are infinitely many angles possible from any point in the universe. You would not see any imaginary sphere however close or far away. But the "fixed" stars can be seen as if they are located on a celestial sphere.
No, it is not.
A plane.
Earth is a deformed sphere. it has large dents all around it. from space you would see white, green, and mostly blue.