As to why Chion asked how to read what Gen wrote...
Gen wrote 因心 which isn't Japanese. It's actually Chinese and pronounced yīn xīn. And since it's not one of words she recognized, she asked how you read it, since people are still making new words and kanji can have several different ways to pronounce it, and maybe if she hears it pronouced, she might recognize it. Nevertheless, the meaning you can still kind of make out by interpolating from the meaning of each words but you might end up with something like, "From the heart" which is pretty close to the Chinese meaning, "goodwill/love."
If you look at the panels, Gen kind of looks around first and writes the word, and then gets super surprised when Chion shows up, so that's a clue to what he was feeling. He wants to write down how he felt about Chion and she basically walked in on him doing it.