Translation:I talk with him about my future career.
Ok, I guess "my future car" is a definite noun and thats why we use fremtidige instead of fremtidig?
Yes, "min fremtidige karriere" is definite.
"The dog" is definite - it refers to a specific dog. "A dog" is indefinite.
It isn't. "Min" indicates a singular noun which is common (an "n-word"). See what MMuhr wrote for the reason why "fremtidig" is in its e-form