Consider a program with argc == 3.
   argv
     |
     v
+---------+         +----------------+
| argv[0] |-------->| program name\0 |
+---------+         +-------------+--+
| argv[1] |-------->| argument1\0 |
+---------+         +-------------+
| argv[2] |-------->| argument2\0 |
+---------+         +-------------+
|    0    |
+---------+
The variable argv points to the start of an array of pointers.  argv[0] is the first pointer.  It points at the program name (or, if the system cannot determine the program name, then the string for argv[0] will be an empty string; argv[0][0] == '\0').  argv[1] points to the first argument, argv[2] points to the second argument, and argv[3] == 0 (equivalently argv[argc] == 0).
The other detail you need to know, of course, is that array[i] == *(array + i) for any array.
You ask specifically:
- Why does **argv point to the first char and not the whole string?
*argv is equivalent to *(argv + 0) and hence argv[0].  It is a char *.  When you dereference a char *, you get the 'first' character in the string.  And **argv is therefore equivalent to *(argv[0]) or *(argv[0] + 0) or argv[0][0].
(It can be legitimately argued that **argv is a character, not a pointer, so it doesn't 'point to the first char'.  It is simply another name for the 'p' of "program name\0".)
- Likewise, why does *argv[0] point to the same thing as the previous example.
As noted before, argv[0] is a pointer to the string; therefore *argv[0] must be the first character in the string.
- Why does *argvpoint to the whole first string, instead of the first char like the previous example?
This is a question of convention.  *argv points at the first character of the first string.  If you interpret it as a pointer to a string, it points to 'the whole string', in the same way that char *pqr = "Hello world\n"; points at 'the whole string'.  If you interpret it as a pointer to a single character, it points to the first character of the string.  Think of it as like wave-particle duality, only here it is character-string duality.
- Why does *argv + 1point a string 'minus the first char' instead of pointing to the next string in the array?
*argv + 1 is (*argv) + 1.  As already discussed, *argv points at the first character of the first string.  If you add 1 to a pointer, it points at the next item; since *argv points at a character, *argv+1 points to the next character.
*(argv + 1) points to the (first character of the) next string.