Let's address the second question first, because it's the easiest to answer. JKR has addressed this herself in an interview:
Will there be, or have there been, any "late blooming" students in the school who come into their magic potential as adults, rather than as children? ...
JKR: ... No, is the answer. In my books, magic almost always shows itself in a person before age 11; however, there is a character who does manage in desperate circumstances to do magic quite late in life, but that is very rare in the world I am writing about.
Barnes and Noble interview, March 19, 1999
While she states that "there is a character who does manage in desperate circumstances to do magic quite late in life", that never actually happens in the books. It appears that's a plot point for a later book that was eventually scrapped. There's a bit of additional information on that in this question.
As for the first question, it's possible for magical ability to be affected to varying degrees by emotional trauma. There are three examples of this in canon:
Nymphadora Tonks. She (temporarily) loses her powers as a Metamorphmagus in the sixth book, after being rejected by Lupin. Since the two were married, and had a child, by the end of the seventh book, she likely would have regained them.
Ariana Dumbledore. She lost the ability to control her magic after being attacked by a group of Muggle children, though she did still retain magical ability.
Merope Gaunt (Voldemort's mother). She spent most of her life being tormented by her father and brother, who believed she was essentially a Squib. However, Dumbledore speculates during his lessons with Harry in his sixth year that her magical talents would have flourished when they were both sent to Azkaban. She would later lose them again after being rejected by Tom Riddle, Sr. while pregnant with their son.