I'm enjoying the confusion of having absolutely no idea what the space suit plotline could possibly be about.
What's the last panel of page 15 about? It seems like a mean thing to say that's seemingly motivated by no reason and followed by no reaction.
It's Shimamura trying to give a little bit of a push to get Adachi motivated to start going to classes. It's not malicious.
To expand on shadesofgreymoon's explanation, "Would you not..." is an (old fashioned) way of propositioning someone. Ex. "Would you not stay for tea?" -> (is equivalent to) -> "Would you like to stay for tea?"
I'm not sure what the original text said, but if I had to guess I'd imagine it was probably something like「行かない?」or「行きませんか」which is similar in that they are also propositions and use the negative form of the verb.