Can a lens affect relative performance of autofocus points?

Yes, lenses can affect AF performance.

Yes, two individual lenses that are the same model number can affect AF performance in different ways. This is because the primary purpose of in-camera autofocus adjustment is to adjust for the result of differences in manufacturing tolerances between individual copies of lenses when they are used on individual copies of cameras.

Calibrating a camera to match it with a certain lens when using a specific AF point, such as the center point, is no guarantee that the camera will be calibrated for other AF points using the same lens.

In fact, calibrating a camera to to adjust AF for a specific point, such as the center point, at a specific focus distance does not even guarantee that the same adjustment will insure accurate focus using the same lens and same AF point at other focus distances. Or even when the lens moves from a longer focus distance as compared to when the lens moves from a shorter focus distance than the distance to the subject. Many lenses will vary when AF is initiated with the lens focused to infinity as compared to when AF is initiated with the lens focused to the MFD. Slight variations from one shot to the next are also normal.

For example, I have a Canon EF 100mm f/2 lens that requires different AFMA (Auto-Focus Micro Adjustment, the name Canon uses for what Nikon calls AF Fine-Tune) settings when used at shorter focus distances than when used at longer focus distances. It's a pain to have to change the AFMA setting to match the distance range at which I'm shooting. But the in-camera AFMA feature only allows for one adjustment per prime lens.

Some Canon cameras allow for two AFMA adjustments for zoom lenses, one for each end of the lens' focal length range. The two correction values are then interpolated for intermediate focal lengths. But as far as I know, no Canon camera allows for multiple AFMA adjustment for the same focal length at different focus distances, much less for different adjustments for each AF point.

Though I'm less knowledgeable about Nikon cameras, based on what I've seen I'd be very surprised if any Nikon DSLRs allowed for multiple AF Fine Tune adjustments of a prime lens, either for different focus distances or for different AF points. Not even the Sigma Optimization Pro software allows for different adjustments for using different focus points at the same focal length and focus distance range, nor does Tamron's similar TAP-in Console software used with the Tamron TAP-in dock.

Notice that above we said calibrating a camera to a specific lens. This is because that is what you are doing with the AF-S Nikkor 50mm f/1.8G when you use the camera's on-board AF-Fine tune capability. AF Fine Tune does nothing to change how the lens responds to an instruction from the camera to move the focus position by a certain amount. Instead, it adjusts the instruction the camera sends the lens when the camera has determined the lens needs to move a certain amount.

On the other hand, using the Sigma Dock and their Optimization Pro software actually changes how the lens responds to various commands from the camera at different focal length and focus distance ranges.

As Roger Cicala, the founder and lens guru at lensrentals.com, often reminds everyone: "There is no perfect lens." This is true in terms of optical performance apart from AF performance, and it's even more true in terms of AF performance. The more one is willing to spend on a design, the more one is willing to spend on tighter manufacturing tolerances, etc., then the less variation one can realize between one copy and the next. But there will always be variation.

Could this be explained by a faulty 50mm lens?

It might be explained by a faulty lens. Or it might be explained by the limits of the design of the lens in question and/or the design limits of the camera. It would all depend on just how much the variation is between different shots taken using the same AF point at the same distance as well as the variation between different shots using different AF points.

So what does this all mean for your situation? Mostly it means you can try and determine why your AF-S Nikkor 50mm f/1.8G behaves the way it does. Only then can you determine what needs to be done to correct it as much as it can be corrected. Some possible things that could be contributing factors:

• Misaligned lens elements, particularly tilt or decentering, which would affect different areas of the frame differently.
• Worn mechanical components, such as rollers, bushings, mis-shapenned grooves in the helicoid collars, etc., in the lens' focusing mechanisms.
• Wear to the lens' AF motor.

With a more expensive lens it would make sense to send it in to Nikon Service to see if they can sort it out. But with the AF-S Nikkor 50mm f/1.8G, unless the lens is still in warranty the cost of any repair will probably be an appreciable percentage of, if not more than, the price of the lens.

Some of Roger Cicala's related blog entries:

Regarding manufacturing tolerances, please see:
This lens is soft and other myths
This lens is soft and other facts
Optical Quality Assurance

For why sensor resolution matters with regard to how well we can see where a lens is less than perfect (and all real lenses are less than perfect, not just in their implementation but also in their design if they are intended to image more than a single wavelength of light), please see:
Why We’re Going to Start Testing Cinema Lenses. And Why We Haven’t Before.

For further reading on AF systems, Roger Cicala's Autofocus Reality series is very insightful: Part 1, Part 2, Part 3A, Part 3B, and Part 4. And: How Auto Focus (Often) Works