I'd have to say no.
For the 1st question:
Can a player cast a spell that has a sphere effect such as fireball or shatter such that only the 8 creatures surrounding the one that is prone be hit?
Since we're assuming a grid is being used, from the DMG page 251 we have
If an area of effect is circular and covers at least half a square, it affects that square.
Under that rule, to avoid the prone creature (assuming size medium), we'd have to have less than half of the 5' cube they control included in the sphere. (The rules don't actually specify the height of grid squares, but for the sake of argument I'm going to assume 5' cubes in 3 dimensions, as discussed in this question.)
Mathematically, if you center a 20' sphere directly above the center of the 5' square controlled by the prone creature, and you set the height so that less than half of that creature's 5' cube is covered by the spell, then the adjacent cubes will have even less of their volume covered (the sphere curves upward as you go out) and would not be affected either.
The 2nd question is moot for me, since I wouldn't allow it.
For the 3rd question,
...is it feasible to have spells cast in such a way so that a body lying prone won't be affected by a spell cast just overhead?
As discussed above, to do so you need to position the spell so that less than half the area the prone creature controls, nominally a 5' cube, is included in the spell.
As an aside, if I'm casting fireball and trying to hit as many of the 8 creatures surrounding a single friendly creature as I can, then prone doesn't really help me. The best you can do is have your spherical area contain just shy of half of their space, which would encompass 3 of the opponents, either 3 on one side of them, or 3 at and next to a corner of their space, depending on where you center the fireball relative to them.
And lastly, back to question 2, should you allow any caster of a fireball or other spherical AoE spell to spare a creature at the center who drops to the ground? Something to consider is that you're providing a feature that is similar to and in some ways more powerful than certain class-specific features.
For example, the Sorcerer Metamagic Careful Spell (PHB p. 102) allows the Sorcerer to spend a sorcery point to allow some creatures to automatically succeed on their save (they would still take half damage from a fireball).
Also, the Wizard School of Evocation ability Sculpt Spells (PHB p. 117) allows the wizard to choose certain creatures to automatically succeed on their saving throws against the spell, and they take no damage if they would normally take half damage on a successful save.
Allowing anyone casting spells to achieve an effect as good or better than class abilities can somewhat undermine some of the uniqueness of your players class choices.