Gascard DuPuis is a blood mage investigating the same murderer that killed Ghislain's wife in Act 1. Hawke initially suspects him to be the murderer but, as suspicious as his methods are, he isn't. Hawke can either take a ruthless position and kill him to eliminate the risk or let him go either out of a desire to help a fellow mage or, perhaps, on the basis that he may be able to provide more information later (he can't, but that assumption is what may guide your hand here.)
Varnell and the Qunari prisoners
Varnell is a Templar fanatic who abducts a group of Qunari dignitaries after they visit the keep. You find him leading a lynch mob, threatening the fragile peace with the Qunari occupiers. Hawke can either take his side, in which case the Qunari are fought and killed, or act against him on behalf of the city, killing Varnell and the mob he leads. Killing the Qunari goes against the Viscount's wishes, so Hawke would need to be fairly committed to a violent path to take that option.
Sister Petrice is behind both the Qunari abductions and the fate of Ketojan in Act 1. She's trying to force a Qunari-Kirkwall conflict to satisfy her particular interpretation of her faith, and in Act 2 that leads to the death of the Viscount's son, Saemus (if he survives Act 1). Hawke can either agree to help her force a conflict or refuse, in which case she's assassinated by the Qunari and the conflict begins anyway. This choice establishes Hawke's level of interest in diplomacy versus fighting, basically.
A weird one, this. You can investigate Hubert's missing caravans in Act 2 but the perpetrator is a bandit, Brekker, not a dragon. As a result Keep's presentation of the quest is a little confusing. If you did it, however, pick the 'discovered looter' option - even if the description is wrong.
You only meet Yevhen if Nathaniel died in the previous game, so disregard this if he survived. The quest involves going to the Deep Roads to rescue a trio of dwarven brothers who followed your example and headed off to find treasure. Once down there, you can only save two of the three - either Iwan or Merin will die. Iwan is kind of a dick, however, and locked his brother in a room full of darkspawn, so Merin is probably the safe choice.
Javaris is an opportunistic dwarven merchant who, in his attempt to discover the secret to Qunari gunpowder, accidentally allows an elven fanatic to release a poisonous weapon in Lowtown. He's culpable but not entirely to blame, so it's down to Hawke's mercy whether or not he survives.
Harley and the raiders
Lieutenant Harley and her company are discovered pinned down by raiders on the Wounded Coast. Assuming that you do find them, you can either abandon them to their fate or agree to help. The safe option for Hawke's party is to charge alongside the guards, but if Hawke is a real hero then it's possible to take on the entire bandit group without the help of the guards, earning greater praise as a result.
Regardless of whether he went to the Circle or the Dalish, Feynriel has become trapped in the fade. He's a Somniari, a mage capable of manipulating dreams, and as such he's too dangerous to leave in his current condition. The outcome of this quest depends on Hawke's actions in the Fade - a little like Connor in Origins. Providing Hawke successfully defeats the Sloth demon, Feynriel is freed and sets off for Tevinter to learn more about his powers. If Hawke doesn't want to take that risk, however, then killing Feynriel in the fade results in him becoming Tranquil - essentially, lobotomised - in the real world. Finally a bargain can be made that allows the demon to retain control of Feynriel, which is a good result for nobody except the demon.
In most cases, a forced confrontation with the Qunari leader will result in Hawke killing them. However, if you really hate Isabella for whatever reason then handing her over alongside the missing tome can secure peace. The Arishok might survive an encounter with a Hawke who is invested in the safety of the city, forgiving of decapitated Viscounts, and who really isn't a fan of pirates.
Next page: Act 3 and Legacy