I think it’s mainly just her emulating her mom and what she understands to be a mother mixed with her personal feelings towards Zen that makes it feel a bit strange. For me, it mainly feels like she does what she does because she cherishes Zen and appreciates her mom’s presence so much that she feels Zen would be lonely without someone like a mom, especially seeing that she feels the need to protect him. Because she thinks he needs protection and ‘a mother’s love’ she does things that wouldn’t seem normal but are now regular happenings in the households. Obviously puberty is changing the situation, which is why I think the manga sets us up in their middle school life.
It's a cute story, but is it just me who finds her actions odd? To be honest I think any average person would find it odd that someone is trying to be their mom when their mother is dead. I know she is doing this because she always wants to be there for him but her behavior would make me uncomfortable. Maybe because his mom passed when he was extremely young she gets away with her actions. Not saying I don't like the manga it is a good read and I'll continue to read but her behavior creeps me out a little. Just wanted to hear others' thoughts on how she behaves.