Actually, you could also marry Lumina, only you have to make her four hearts by the first year, and wait until she comes to your house at the end of the first year. Don't give her the blue feather cause she won't accept it. Still, because she is too young, you could not marry her in the first year, so you';; get to marry her in the second chapter, where she'll be growing older.
No, that's not true. Lumina's not one of the choices...
I think you're thinking of a different game here...
The only game you can marry Lumina in is Harvest Moon: Oh! A wonderful Life.