1. When they were about to have the ranking match, Oishi objected to having Tezuka back and challenged Tezuka, citing as reason if the team that got through Regional together is suddenly disrupted, it is not good for team morale, and that he couldn't allow anyone back on the team whose injury hasn't healed completely. Tezuka could not allow Oishi a single game, or he would not be allowed in the ranking match. Turns out Oishi's injury from before Hyoutei match hasn't healed completely. So Tezuka wins 6-0. Oishi later apologizes to him, saying he had to do it, and Tezuka says he understands. Do you want a link to the relevant translation?

2. Tezuka was vice-captain. Inui mentions this during Hyoutei match, I believe, that Seigaku's then-captain lost, but Tezuka, as vice-captain, won.

3. Doesn't strike a bell. At least, not a complete bell. A little more context?

4. Oishi's uncle is a doctor, the same one Tezuka goes to in manga/anime. Oishi's also the top student in his year.

If you want more specific references, let me know?