Should an observation always belong to the population to calculate its z-score? It was mentioned in this link that,

the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured.

i.e. $z(x) = (x - \mu) / \sigma$
where,
$z(x)$ = z-score of $x$
$x$ = observed value/observation
$\mu$ = population mean and
$\sigma$ = standard deviation of population
Should the observed value/observation always belong to the population and why ?
Eg: Say 4 stores A,B,C and D have some number of customers in their store (say a,b,c and d number of customers respectively) and the mean and standard deviation of the number of customers in A,B,C,D are $\mu$ and $\sigma$ respectively (i.e. mean(a,b,c,d) = $\mu$ and standard_deviation(a,b,c,d) = $\sigma$). From examples that I have seen, we generally find the z-score of a,b,c or d (i.e. z(a) or z(b) etc.). Consider another store E with e number of customers. Then, can we calculate the z-score of e with respect to $\mu$ and $\sigma$ OR can we only calculate the z-score of a,b,c or d with respect to $\mu$ and $\sigma$ and why ?
 A: Maybe we should rephrase the question. Obviously we can compute a $z$ score for whatever we want. The question  is whether or when we would choose to do so.
One obvious reason to compute a $z$ score is to perform a test, whether any given observation can plausibly follow a given distribution. Sometimes you compute the $z$ score just to demonstrate that an observation can not plausibly stem from a given normal distribution.
In your example: We have a shop A with a given mean and standard deviation of costumers per month. Now we open shop E and in the opening we put a lot of effort into considering astrological advice (opening at waxing moon and whatnot). So we expect the first month customer count to be well above that from store A.
We might compute the $z$ score of our first month for E  with the mean and sigma taken from A just to demonstrate the superiority of E over A.
In that example we'd compute E's $z$ score: not because we think it comes from a different distribution, but because we want to show that it comes from a different distribution.
