Systems of inequalities in n variables with create an n-dimensional shape in n-dimensional space which is called the feasible region. Any point inside this region will be a solution to the system of inequalities; any point outside it will not.
If all the inequalities are linear then the shape will be a convex polyhedron in n-space. If any are non-linear inequalities then the solution-space will be a complicated shape.
As with a system of equations, with continuous variables, there need not be any solution but there can be one or infinitely many.
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Yes.
If the lines intersect, then the intersection point is the solution of the system. If the lines coincide, then there are infinite number of the solutions for the system. If the lines are parallel, there is no solution for the system.
Yes.
If it is joined by an "and" it does. If it is joined by an "or" it does not.
There is only one solution set. Depending on the inequalities, the set can be empty, have a finite number of solutions, or have an infinite number of solutions. In all cases, there is only one solution set.