What is the size of a pointer?
Solution 1:
Function Pointers can have very different sizes, from 4 to 20 Bytes on an X86 machine, depending on the compiler. So the answer is NO - sizes can vary.
Another example: take an 8051 program, it has three memory ranges and thus has three different pointer sizes, from 8 bit, 16bit, 24bit, depending on where the target is located, even though the target's size is always the same (e.g. char).
Solution 2:
Pointers generally have a fixed size, for ex. on a 32-bit executable they're usually 32-bit. There are some exceptions, like on old 16-bit windows when you had to distinguish between 32-bit pointers and 16-bit... It's usually pretty safe to assume they're going to be uniform within a given executable on modern desktop OS's.
Edit: Even so, I would strongly caution against making this assumption in your code. If you're going to write something that absolutely has to have a pointers of a certain size, you'd better check it!
Function pointers are a different story -- see Jens' answer for more info.
Solution 3:
On 32-bit machine sizeof pointer is 32 bits ( 4 bytes), while on 64 bit machine it's 8 byte. Regardless of what data type they are pointing to, they have fixed size.
Solution 4:
To answer your other question. The size of a pointer and the size of what it points to are not related. A good analogy is to consider them like postal addresses. The size of the address of a house has no relationship to the size of the house.