The following dialogue options seem to be required to get the Q award (or Ned Defender or J'Accuse) at the end of the game. Not 100% sure of this but I've done a lot of testing and feel pretty good about it. Specifically, it's impossible to pick a lesser subset of these dialogue options and still get the Q, J'Accuse, and Ned Defender awards. It might be possible to pick some lesser subset plus some unincluded dialogue options which I've determined to be not necessary to getting the awards, but I don't think the chances are very good. Always worth further exploring, though.

Dialogue options marked with ~ are necessary for Q. > means either Ned Defender (asking Daryl about Connie, immediately followed by saying that you're not interested) or J'Accuse (telling Connie that Jake knew she won the judo competition). = means it's necessary for getting the boiler room note and thus is necessary to complete the game (so it's necessary no matter what).

Hulk: ~Connie (meet Connie) Tough time? ~Hal (meet Hal) Friend of Jake? =Robbery at pharmacy (read newspaper in locker) =Injury (talk to Hal about Hulk) ~Jake knew you broke into the pharmacy (watch Jake's first video) What did he want from you? Did you kill him?

Connie: ~Dating Jake (ask Hal about Connie) ~Hal (meet Hal) ~Money's tight? (ask Hulk about Connie) =Crane medallion (check judo poster, read kanji book) ~Broke date with Daryl (find note at Maxine's) >You won the judo competition (watch Jake's first video) Jake was threatening to expose you

Hal: ~Connie (meet Connie) ~Daryl (meet Daryl) ~Like his father? (after above dialogue option) =Hulk (meet Hulk) =Plagiarized the essay (check book in Jake's locker, Hal's essay in teacher's lounge) ~Connie says you study too hard (ask Connie about Hal)

Daryl: ~Found Jake's Body (ask Hulk about Daryl OR ask Connie "who found the body" during intro convo) >Connie (meet Connie) >Thanks for the compliment but ~Connie broke off date (find note at Maxine's) ~Soaping windows (security report in teacher's lounge I think?) ~Dad owner of Gray Enterprises (read about Daryl's dad in teacher's lounge) ~Gray Enterprises bankruptcy (ask Hal about Daryl's dad) ~Hal said Daryl met with Jake (talk to Hal about plagiarizing the essay) ~Hulk saw envelope delivery (talk to Hulk about being blackmailed by Jake)

Beech is 100% skippable lol Calling Mitch back is also unnecessary.