How big is the capacity of a standard memory cell that the pointer is linking to?
That depends on the underlying architecture. Most machines today use byte addresses, but machines that addressed words (i.e. 16, 18, 32, even 36 bits) were reasonably common. If I recall correctly, most RISC machines were unable to address anything but words (but gave addresses in bytes). At least, such an address caused the CPU to fetch both words and snip out and assemble the piece wanted.

What your favorite language does above the machine's intrincacies, ask them. Often they will refuse to handle pointers that aren't aligned at some "machine natural boundary", like the size of a C double, 8 bytes. Even on machines that have no penalty attached to non-aligned address acces.