As I am learning virtual memory, I am confused about the size of the addresss space and page size. Assume that we have a $32$ bit address space. I can see that it means each virtual address is represented in $32-$bit format and there are, in total, $2^32$ different $32-$bit virtual addresses. So here is my question:

Why the address space is described to be $2^32$ byte? As far I as I remember, each byte is $8$ bit, so each virtual address is $4$ byte. So why the address spcae is $2^32$ times $4$ bytes $=2^34$ bytes?

Also, when we are talking about the page size, assume the offset has $12$ bits, can I say that each page contains $2^12$ different $32-$bit virtual addresses?

Could you please help me with the clarification of the concept?