Neither is deprecared, and with GPU-side pixel buffers I can imagine that drawing pixel rectangles are much more efficient than before. I have not looked into pixel drawing in the modern era though, so I would like to know how modern use of pixel rectangles actually perform.
2. Yes, but as I am trying to point out, there is a huge difference between e.g. glDrawPixels and glDrawElements.
One is deprecated OpenGL 1.2 functionality, which is an entirely different pipeline (with kernels, color matrix and whatnot, see imaging subset) that has always been kind of of half-heartedly supported.
The other is the fully accelerated, native way of drawing textured geometry (such as a quad) using dedicated hardware.
Which, on my system, makes a difference of roughly 1 to 10. Your mileage may vary.
edit: Actually, I take part of the above back: glDrawPixels itself is in fact deprecated. I realized that shortly after posting. There is, however, glBlitFramebuffer for somewhat the same functionality instead.