Is it possible for a program to get number of spaces between command line arguments in POSIX?
In general, no. Command line parsing is done by the shell which does not make the unparsed line available to the called program. In fact, your program might be executed from another program which created the argv not by parsing a string but by constructing an array of arguments programmatically.
It's not meaningful to talk of "spaces between arguments"; that's a shell concept.
A shell's job is to take whole lines of input and form them into arrays of arguments to start commands with. This may involve parsing quoted strings, expanding variables, file wildcards and tilde expressions, and more. The command is started with a standard exec system call, which accepts a vector of strings.
Other ways exist to create a vector of strings. Many programs fork and exec their own sub-processes with predetermined command invocations - in which case, there's never such a thing as a "command line". Similarly, a graphical (desktop) shell might start a process when a user drags a file icon and drops it on a command widget - again, there's no textual line to have characters "between" arguments.
As far as the invoked command is concerned, what goes on in a shell or other parent/precursor process is private and hidden - we only see the array of strings that standard C specifies that main() can accept.
No, this is not possible, unless the spaces are part of an argument.
The command accesses the individual arguments from an array (in one form or another depending on programming language) and the actual command line may be saved to a history file (if typed at an interactive prompt in a shell that has history files), but is never passed on to the command in any form.
All commands on Unix are in the end executed by one of the exec() family of functions. These take the command name and a list or array of arguments. None of them takes a command line as typed at the shell prompt. The system() function does, but its string argument is later executed by execve(), which, again, takes an array of arguments rather than a command line string.