From what I’ve heard, she moved back to her hometown after the divorce.
By circumstance this is your hometown. Not much to say other than it's your hometown and birthplace.
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.
While こきょう is the more common reading for this word, it can also be read as ふるさと, which is a native Japanese word that originally didn't have kanji. ふるさと is also common in hiragana.