I feel this might be a weird/stupid question, but here goes...
In the question Is NULL in C required/defined to be zero?, it has been established that the NULL pointer points to an unaddressable memory location, and also that NULL is 0.
Now, supposedly a 32-bit processor can address 2^32 memory locations.
2^32 is only the number of distinct numbers that can be represented using 32 bits. Among those numbers is 0. But since 0, that is, NULL, is supposed to point to nothing, shouldn't we say that a 32-bit processor can only address 2^32 - 1 memory locations (because the 0 is not supposed to be a valid address)?
the NULL pointer points to an unaddressable memory location
This is not true. From the accepted answer in the question you linked:
Notice that, because of how the rules for null pointers are formulated, the value you use to assign/compare null pointers is guaranteed to be zero, but the bit pattern actually stored inside the pointer can be any other thing
Most platforms of which I am aware do in fact handle this by marking the first few pages of address space as invalid. That doesn't mean the processor can't address such things; it's just a convenient way of making low values a non valid pointer. For instance, several Windows APIs use this to distinguish between a resource ID and a pointer to actual data; everything below a certain value (65k if I recall correctly) is not a valid pointer, but is a valid resource ID.
Finally, just because C says something doesn't mean that the CPU needs to be restricted that way. Sure, C says accessing the null pattern is undefined -- but there's no reason someone writing in assembly need be subject to such limitations. Real machines typically can do much more than the C standard says they have to. Virtual memory, SIMD instructions, and hardware IO are some simple examples.
If a 32-bit processor can address 2^32 memory locations, that simply means that a C pointer on that architecture can refer to 2^32 - 1 locations plus NULL.
First, let's note the difference between the linear address (AKA the value of the pointer) and the physical address. While the linear address space is, indeed, 32 bits (AKA 2^32 different bytes), the physical address that goes to the memory chip is not the same. Parts ("pages") of the linear address space might be mapped to physical memory, or to a page file, or to an arbitrary file, or marked as inaccessible and not backed by anything. The zeroth page happens to be the latter. The mapping mechanism is implemented on the CPU level and maintained by the OS.
That said, the zero address being unaddressable memory is just a C convention that's enforced by every protected-mode OS since the first Unices. In MS-DOS-era real-mode operaring systems, null far pointer (0000:0000) was perfectly addressable; however, writing there would ruin system data structures and bring nothing but trouble. Null near pointer (DS:0000) was also perfectly accessible, but the run-time library would typically reserve some space around zero to protect from accidental null pointer dereferencing. Also, in real mode (like in DOS) the address space was not a flat 32-bit one, it was effectively 20-bit.
It depends upon the operating system. It is related to virtual memory and address spaces
In practice (at least on Linux x86 32 bits), addresses are byte "numbers"s, but most are for 4-bytes words so are often multiple of 4.
And more importantly, as seen from a Linux application, only at most 3Gbytes out of 4Gbytes is visible. a whole gigabyte of address space (including the first and last pages, near the null pointer) is unmapped. In practice the process see much less of that. See its /proc/self/maps pseudo-file (e.g. run cat /proc/self/maps to see the address map of the cat command on Linux).
