It was him though, he was the one who sent the message.
His message just said "I'm sorry/it's all my fault", she's the one who pushed things to the "let's make up" stage. But also I kind of agree in that this arc is (hopefully) him growing up a bit and not waiting around for choices to be made for him.
No, their point was that she can't feel love at all.
B/c she's selfish, which like I also think what Aya feels towards Yuu is more the dopamine high love of having a toy that makes her feel better than a healthy love that treats him as a whole person. The constant deflection, the ghosting, the potentially blowing things up his relationship w/ Hikari by kissing him - Aya consistently chooses her own comfort/safety/feelings over Yuu.
And yeah I think this is all supposed to be strong parallel to her mother, who always chooses the men in her life over Aya. The tragedy of Aya falling into the same patterns that have made her life so miserable.