You don't pay much attention to the manga do you? Ikumo was Ichigo's boss, not Captain of the baseball team.
Ichigo emo? He wasn't emo-ing at anything. He just forgot his badge there cause the poor guy had a lot on his mind. He was invited to the Reiokyu, met with the Royal Guard members, was given hope that his Bankai could be re-forged but when he failed the test he was kicked out without a seconds hesitation. If you give anyone hope and then take it away, you're bound to hurt them mentally/psychologically. He feels powerless and useless - something that Ichigo fears above all else as we saw during the Xcution Arc.
I don't think the revelation that Ichigo was a Quincy was the main point of the Isshin/Ichigo face-to-face. The main objective of the conversation and flashback isn't that Ichigo is part Quincy - we already know this. The point was to show how Isshin and Masaki met and to reveal Isshin's connection to the Gotei 13. Nor was Isshin approaching Ichigo in any way awkward and ill timed. Ichigo told Isshin that he could reveal the truth to him when he felt the time was right. He said this way back when Isshin confronted Aizen and Ichigo saw that he was a Shinigami for the first time. The timing was perfect in my opinion.