The role of grain in accutance is fairly well known, and most printers recognize that prints with some apparent grain appear sharper than prints without apparent grain.
What is sharpness?
Lets think of a dark grey object on a light grey background.
Sharpness is a physiological phenomenon that can be tracked down to Detail Contrast. There are several ways to enhance Detail Contrast and thus enhance Sharpness.
One is resolution. The higher the resolution, the more precise and harder
can the borderline between the dark grey object and the light grey background been modelled.
The second one is print contrast. Everybody knows that prints on higher paper grades usually look sharper than the same print on a lower grade paper. A low contrast scene like a tree in the fog remains relatively unsharp, even if taken on TP and print on a grade 5. Paper grade affects the difference between the dark grey object and the light grey background so that the eye and the brain recognise the borderlines worse or better. In the extreme cases, the light grey background becomes white and the dark grey object becomes black or both are mapped onto nearly the same grey tone on the print. Color contrast can do the same thing on a color print. The borderline between red and green is always sharper than, e.g., blue and violet.
Acutance is a trick that increases the contrast directly at the borderline between the dark and light grey areas. Unsharp Masks and DIR-Couplers are other examples that work the same way. They aid the brain to better perceive the borderlines such that the image processor
in our brain can calculate
a clearer vision which makes us think that it look sharper. If you look at the MTF-Diagram in the Tech Specs of e.g. Kodachrome, you will see that at 5 lp/mm the output contrast is significantly higher than the input contrast, which means that this film is partially sharper than reality!
Third, there is a certain, not exactly determinable, physiological phenomenon that makes us think that a coarse structure is sharper than a smooth one. This adds some virtual sharpness
to a grainy print which is objectively not there.
1) How does grain structure affect the appearance of an image if it is invisible?
It does not. Very small and invisible grain does increase resolution and thus provide a more precise way to separate things for the eye and brain. See above.
2) Would the apparent sharpness of a contact print be improved by visible grain?
See third point above
4) How does grain structure affect edge effects?
The sharper the edges of the grain the clearer are the borderlines between grain and no grain. Look at color film. Color film does not have grain. All the grain is removed in the bleach and fix. What is left are tiny dye clouds that have been developed together with the grain. On very high mag. ratios, these clouds look rather pointilisic with no edges at all.