Not really sure what the exact issue is. Is it that everything is offset by half a block?

What exactly do you mean by "equidistantly" here?

Oh, I did not see the distinction. In fact had to reread your text a few times, I think I get it now. Is this Unity-specific?

That sounds like an underlying bug that desperately needs fixing

What do Cp, Cm and the sigma_Cp, Cm things stand for?

Does this answer your question? How can I implement an inventory that stores different types of items?

+1 for this. Keep the "actual" x,y,z capped at something low-ish like 32 or 256 so that local floating point math stuff can take your numbers "as is" with at most double the stride amount in the integer part, which keeps precision usable, and then the second set of X,Y,Z - 64 bit ints that specify grid position. Most "hard" math happens on the floats which both the GPU as well as the CPU's ALU are already optimised for.

An MMORPG I used to frequent had an issue of there being too many situation specific items - despite having 2 different (up-to) 80 slot "banks" plus an up-to 64 slot inventory, it would fill up with things like all kinds of time-gated tokens (to prevent people from spamming a dungeon it would require one of these to run, and you'd only get one once a day), all kinds of dungeon-specific currencies, rare, but hard to sell crafting ingredients, and a bunch of other "only useful if you have 100+ of it" hoarding type things. A lot come in tradeable and nontradeable form - that's 2 separate stacks.

I am not 100% sure I understand this. When no input is provided, does the paddle just follow the ball? Or it stays put, but rotates to face the ball?

This will definitely require a lot of tweaking and playtesting. It may also be a game mechanic without mass appeal. There hasn't been any obvious feedback from OP yet, perhaps I missed the mark entirely, or was right on point, or right in between.

I also suggest to have some vague direction to it so that it is possible to "hint" towards specific effects. Perhaps a few pre-existing spells to ease the player into the system could be a good idea.

@Mars second to last paragraph, OP wants something that isn't easy to figure out. Unpredictability means there's no telling what the result will be of any particular combination, but the outcome is always the same so once the player learns a good combination they can reuse it.

huh, never heard of this game before, that system is surprisingly complex. I do think that the "back end" of it is what OP wants, but the interface seems to be more programming - like which is what they want to avoid.