A space can be two-dimensional and infinite if it does not have defined bounds. Mathematically, this usually means no restrictions on the domain or co-domain of the two-dimensional space.

zero. two dimensional figures do not occupk any space

No.

Many of us have experience with two dimensional space. We create graphs on 2-D space. Take a sheet of paper, draw an x and a y axis on it, and go to town. This two dimensional space is as real as three dimensional space around (and including) it.

A solution (in 2-dimensional space).

A solution (in 2-dimensional space).

A solution (in 2-dimensional space).

A solution (in 2-dimensional space).