char array[8] = "Raining";
I think all the below comments respective to the statements are true to my understanding.
char *p1 = array + 7;      --> points to '\0'
char *p2 = array + 8;      --> undefined behaviour
char *p3 = array + 9;      --> undefined behaviour
char *p4 = array + 10;     --> undefined behaviour
Is my understanding correct?
In your case,
  char *p1 = array + 7;
and
  char *p2 = array + 8;
are valid, because, you are legally allowed to point to
OTOH,
  char *p3 = array + 9;
and
  char *p4 = array + 10; 
are undefined.
Quoting C11, chapter §6.5.6, "Additive operators" (emphasis mine)
[same in C99, chapter §6.5.6/p8, for anybody interested]
When an expression that has integer type is added to or subtracted from a pointer, the result has the type of the pointer operand. If the pointer operand points to an element of an array object, and the array is large enough, the result points to an element offset from the original element such that the difference of the subscripts of the resulting and original array elements equals the integer expression. In other words, if the expression
Ppoints to thei-th element of an array object, the expressions(P)+N(equivalently,N+(P)) and(P)-N(whereNhas the valuen) point to, respectively, thei+n-th andi−n-th elements of the array object, provided they exist. Moreover, if the expressionPpoints to the last element of an array object, the expression(P)+1points one past the last element of the array object, and if the expressionQpoints one past the last element of an array object, the expression(Q)-1points to the last element of the array object. If both the pointer operand and the result point to elements of the same array object, or one past the last element of the array object, the evaluation shall not produce an overflow; otherwise, the behavior is undefined. [...]
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