Are draw calls executed in parallel or sequentially or both?
The result should be as if it was executed sequentially one triangle at a time. This is important so that each frame is deterministic. If it wasn't then drawing the same frame multiple times could create different results and create a flickering image on screen.

However that does not mean parallelization is impossible. Vertices can be computed in parallel. Their results will be ordered and fed to the rasterizer which will feed the fragment shader stage.

The same happens with pixels. Typically a group of pixels from a triangle can be computed in parallel and blended. A non-overlapping triangle can then also be filled at the same time however if triangle overlaps one currently busy then the result of the fragment shader must be buffered until the corresponding pixels of the previous triangle are done so blending can happen in the correct order.