No.
There is zero performance benefit in doing this, and creating complex shapes with brushes is more likely to result in map leaks or bad geometry generated (e.g. missing triangles). The result will also look bad because the level of detail you can create with large flat surfaces is low, and there is no smoothing applied, so the results will look more like Thief 2 than a modern game.
Not as far as I know. You can copy textures from different surfaces using various combinations of mouse button and modifier key, which might help in some situations, but I've never seen any way to project textures based on the camera position.
I suppose this would be useful if you wanted to create a flat but non-rectangular shape (like a trapezoid door) and you wanted the texture to align to the edges of the patch. If the flat patches are rectangular I don't see how this would be any better than just putting the texture on the brush itself.
Of course for non-flat surfaces, patches (with caulk brushes behind if needed) are definitely the way to go if you can't or don't want to use a 3D modelling tool.