I’m a bit homesick.
The nostalgic melody made me homesick.
This puppy may be crying because he is homesick, but who cares?
You have your home village and your heart. Your heart always resides in your home village, so when you leave you feel homesick.
Young people don't really use this word anymore. It's more for the oldies. If you're an oldie, go right ahead. If you're a youngie, then talk to more oldies!
The readings are double kun'yomi. The kun'yomi reading is what you learned with 里 already, though you'll have to pull out the 心 vocab reading to remember it all. Not only that, the 心 gets rendaku'd here making it ごころ. Make sure you watch out for that.