I'm looking for software which can help me to visualize 2d and 3d objects in space with additional elements like in examples below.
Also I'd like to rotate 3d figures to be able to look from another angle (make projections with no effort).
Allows placing and labeling points, polygons (including triangles), circles, angles among many other elements.
Includes a 3D View (you have to show it via the menu), which can be rotated and scaled. You can visualize planes by their respective equation. In case you meant orthogonal projections, I guess you can simply let fall a perpendicular through a given point. The latter is at least supported in 2D.
You can export your view to many formants, including PNG and EPS.