You're right its not a Pareto improvement but I'm wondering if its a gain from the point of social efficiency, because overall surplus has increased. And its behen, not bhai :)
q.AVC=TVC, unless MC=AVC, we can't say q.MC=TVC. Or may be my basic is failing me here:/
YES KEY IS REQUIRED FOR BOTH PEA AND PEB!!
For 24th, As the monopolist is operating in the elastic part in market 1, and inelastic in market 2, raising p2 will definitely raise profits. I didn't calculate here as it seemed pretty obvious :/