C’est à vous, ce stylo ?; Ah oui, il est à moi, merci.
Are both these sentences correct?

C’est à vous, ce stylo ?
Ah oui, il est à moi, merci. (This sentence is also referring to the pen - le stylo.)

Is the "il est" form strictly correct and the "c'est" form just a more casual construction? Or else why does one sentence use "il est" and the other use "c'est"?

Question

C’est à vous, ce stylo ?; Ah oui, il est à moi, merci.
Are both these sentences correct?

C’est à vous, ce stylo ?
Ah oui, il est à moi, merci.  (This sentence is also referring to the pen - le stylo.)

Is the "il est" form strictly correct and the "c'est" form just a more casual construction?  Or else why does one sentence use "il est" and the other use "c'est"?

Answer

It is a "casual form"

Answer

In you're example I would say

Il est à vous ce stylo? 
Oui c'est le mien