Why would she? Moeko set things up intentionally for them, and then went off home, having completed her wing-woman role. She lied about intending to go to Yamada's and her brother's condition, most likely, just so Ichikawa wouldn't question anything. She's probably the most astute character in the cast (and clearly supportive of her girl's relationship, ever since figuring it out, likely because of how much she likely gushes about the boy), especially considering the interaction Ichikawa had with her on New Year's Eve, relating to the encounter with Pickup-pai that day (Nanjou Haruya, the senpai 3rd year who's graduating in a few months, in-manga as of these chapters, and shows up every so often to try and get it on with Yamada before he graduates, not yet realizing it's a lost cause already for him because she only has eyes for Ichikawa).
The main concern is if Yamada's parents come home too early. This is not the situation for him to meet the parents in, wearing her PE clothes and all. It is soon, though.
Oh, definitely. To be honest, it should have been kind of obvious, considering how large Anna herself has been proven to be growing up (let us direct attention to Ch6.1, first page, where there's splash art of her in her 5th grade class, towering over her classmates, and clearly already developing in the chest area a bit). After all, where do you think she got those genetics? Her mother doesn't seem all that disproportionately large, after all (in fact, from what I can tell of visuals with her next to her mother, Anna is taller than her- think about that: a woman's 14 year old daughter is taller than her), so it must come from the other side.
Though, to be fair, I'm a giant beanpole, and my parents were relatively normal-sized. The tall genes came from further back in the family and skipped a generation. But it works better in a fictional story to have that sort of thing more directly passed down to hammer it home it's a genetic thing.