Usually I have a vague feeling of when Italian wants articles and when it does not, but in this case I'm surprised that there is no article.
I feel you could probably write in both ways. At least, it sounds correct to me.
Why is 'I shall be an engineer' not accepted as correct?
I am to be an engineer... Sounds right to me
Why " I will be engineer" is incorrect?
It's "ingeniere"...it comes from "genio"(genius)...
No it isn't. It's "ingegnere", as any dictionary will tell you. "Ingeniere" is a common mistake. "Ingegnere" comes from "ingegno", and that from Latin "ingenium".