Technically, the white lines are your image formed by light; the black lines are a lack of light. And what you need is 290 airy disks/mm; which is airy disks of 3.45um in diameter, which requires a perfect lens at f/2.6 or an extremely good lens at f/2 or less.

An airy disk looks something like this where the height equates to the illumunance of the light. The airy disk is the central peak, and the waves are the diffraction pattern caused by the aperture restriction. The diffraction pattern reduces contrast, and when the airy disks overlap resolution is reduced (e.g. 4 airy disks combine/resolve as one).

But even if the airy disks are well resolved and match the size of a photosite, what are the chances that they will perfectly align (extremely slim)? What happens if they don't (moire patterns/aliasing)? And What resolution do you actually need (detail in subject/size of output)? Typically what you really want is a sensor of greater resolution than the scene/lens/need for increased oversampling/accuracy. What do you actually need resolved? Probably not more than 14MP, and most likely less.

And understand that lens resolution ratings are typically sensor dependent. E.g. if a lens resolves 2um airy disks, a sensor with 4um photosites cannot see them individually. So comparing MTF of lenses between systems is not as simple as just comparing the lp/mm results. And IDT it is possible to answer your third question with the information provided. But one thing that holds true is that larger sensors can resolve more. This is because; for the same sensor resolution (MP) the photosites are larger, which is less demanding of lens resolution. Or similarly; if the lens is of equal resolution, more photosites of the same smaller size can be fit on the larger sensor (to match the lens).

To answer your first two questions:

1. As the airy disks bleed over into the dark areas they will both shift towards gray, but the dark areas will become gray more quickly than the white areas will (due to the logarithmic nature of exposure).

2. The decrease in corner resolution is not linear. Understand that the corners of a rectilinear image typically come from the very edges of the projected image circle, and what typically causes the reduction in MTF is a loss of light/contrast at the periphery (vignetting)... the 50 part of MTF50 stands for 50% contrast. There is also often field curvature contributing as well (due to the curved lens projecting onto a flat surface). But macro lenses are typically designed with flat field focus (or moreso).