Many graphics cards/chipsets/etc. do accelerate 2D operations, unfortunately there's no feasible unified model of a "2D hardware accelerator" the way there is with 3D, so there's no unified support for it in kernel, either. The whole thing is inherently hardware-dependent.
Not anymore; at least not like they used to in 90's and 2000's. Today, they expose some overlays (and some limitations, how they can be used) and that's it.
There is a Nvidia OpenGL extension NV_path_rendering that was intended for accelerating 2d, but it wasn't widely adopted.