I've noticed that in my French practice I never say "il est un" or "elle est une". I would always say either "il/elle est" or "c'est" or "c'est un/une".
So far this does not seem to have caused me to have any problems.
Are there any times when I should be saying "il est un" or "elle est une"?
Nowadays, using il est un / elle est une is typical from non native French speakers.
This form is not a grammatical mistake. It sounds archaic but might still be used in formal or literary contexts with the meaning "there is a". It is never required.
See this reply to a question very similar to yours and that explains why c'est un(e) took the lead: https://french.stackexchange.com/a/14729/1109
Are there any times when I should be saying "il est un" or "elle est une"?
Almost: Il est une heure ;-)
No, it means the same. My theory for that is simple, as « C'est un/une » or « Il/elle est » is shorter to say, it gets adopted and used a lot more in verbal's form.
