Lens speed and stopping down lenses to increase sharpness

My 50mm f/1.8 seems to be sharpest starting around f/4. My Sigma 18-125 f/3.5-5.6 seems sharpest starting around f/8. I've read countless posts talking about stopping down lenses to achieve maximum sharpness. This raises two questions as I consider my next purchase:

1. Are there any lenses that are sufficiently sharp wide open?
2. If one were to compare a 2.8 lens that is sharp at f/4 to a 4 lens that was sharp wide open, would the 2.8 lens have any added value for low-light shooting?

1. Yes, but generally they tend to be more expensive.
Keep in mind, when shooting below 2.8, you depth of focus is thin, paper thin below f/2.

2. Depends how soft. Generally the 2.8 should beat out the 4 lens that is wide open. Always depends on the products you compare and their quality. Soft is better than no shot and post processing can make up for a lot of things if you get down the exposure and still are in focus.

Define "sufficiently sharp". If you mean "at their absolute sharpest", no. If you consider "sufficiently sharp" as "sharp enough to get a good print of the desired size", there are many.
The f/2.8 lens would give you an additional stop of shutter speed for improved hand-holdability. The lens quality isn't the only factor that goes into image quality. A sharp lens that forces you to use a slow shutter speed so you get camera motion blur isn't doing you any favours.

Thanks for the input. That helps clear things up for me.