Prologue
No major decisions to be made here. Hawke needs a sponsor to get his family into Kirkwall, and your options are a group of smugglers or a legitimate mercenary company. The latter might be the choice of a warrior Hawke, while the former makes more sense for rogues, but they really don't affect much. Mages are offered protection either way.
Act 1
Many of Keep's tapestries are confusingly laid out, but Dragon Age 2's are particularly so. For that reason I'm going to group decisions in terms of related quests - I imagine that many of the problems people have with the site come from not remembering which characters go with which decisions. For example, the outcome of the Starkhaven mage storyline and the fate of the Templar involved (Karras) are at opposite ends of the grid for no discernable reason.
What did Hawke do with the Templars?
A hunt for some missing Starkhaven mages comes to a head when their leader turns to blood magic just as Templars threaten to barge in and lead them away. Hawke can either fight the Templars' leader, Karras, with the help of a lenient Templar, Thrask, or persuade them to leave. Alternatively, a pro-Templar Hawke might simply hand the mages over. This is the first decision you make that indicates Hawke's leaning one way or the other in the mage/Templar conflict - so consider your choice of class, and your relationship with your sibling, when doing so.
Karras' fate
If Hawke chooses to fight Karras, he is killed with minor consequences in Act 2. Otherwise, he lives.
Saemus' fate
You're sent to rescue the Viscount's son from the Qunari but find that he has joined the Qun willingly. In order to return him to Kirkwall you must fight another mercenary company, the Winters, who are threatening his life having just killed his Qunari protector. If you don't resolve the quest, Saemus dies.
Ginnis' fate
Ginnis, the leader of the Winters, is killed if you rescue Saemus. If you don't do the quest, she lives.
Martin's cargo
If you help Isabella's friend Martin track down some stolen cargo in the docks he turns into a shop. Who doesn't like shops? Or Isabella?
Kelder's fate
Kelder is a serial killer preying on elven children. When you head out to track him down, his father - an important magistrate - begs you to show mercy. On the other hand, the father of one of the victims demands justice.
When you find him (in the Deep Roads for no discernable reason) he's been humbled by his latest near-victim, an elven child who also begs you to spare his life. However, it's not clear that he's entirely free of his compulsion to kill and even he concedes that he could be a danger again. Killing him isn't a totally unreasonable proposition, considering that his father is likely to help him avoid justice in the courts. On the other hand, this means killing him in cold blood against the wishes of a powerful man. One to mull over.
Feynriel
You're asked to track down a young half-elven man who has just discovered his magic. Finding him, you can either advise him to return to the Circle - a little hypocritical for a mage Hawke, or one that is busy protecting his sister from the same - or suggest that he goes to his mother's people, the Dalish elves. Either way he returns in Act 2, so this is chiefly about establishing Hawke's instinctive allegiances.
Danzig's fate
Danzig is a Tevinter slaver you encounter during the search for Feynriel. It's possible to shake him down for information and spare him, or kill him outright. A fight is quite a likely outcome here, given what a tremendous asshole he is. Nonetheless, it is possible for him to survive if Hawke is feeling particularly clement.
Ghyslain's wife
The first part of a murder mystery that will come back to haunt Hawke in Act 2. Ghyslain is a slimy nobleman who wishes to understand why his wife has disappeared - more to protect himself from accusations from her family than out of concern for her well-being. You find her brutally maimed body after a short investigation, and have the option of protecting him from the grisly truth or shaming him by telling him outright. Presuming you do this quest, of course.
The missing miners
Hawke can end up rescuing miners from the Bone Pit out of a desire to help fellow Ferelden's or simply for the cash, but his motivations don't matter here - this is another 'did you do this?' choice.
Bribing Thrask
During the course of another investigation Hawke discovers that the daughter of the moderate Templar, Thrask, is an abomination - right after Hawke kills her. You can use this information to shake Thrask down for money or keep his secret to secure his loyalty. If Hawke really hates Templars (or loves gold) then the former is a likely option, whereas the latter is the politically savvy move.
Idunna's fate
Idunna is a blood mage posing as a prostitute involved and seducing and abducting Templar recruits on behalf of a band of apostates. She attempts to mind control Hawke and fails, either due to Hawke's own magic or that of his allies. You can then choose to kill her or hand her over to the Templars - an anti-Circle Hawke, or simply a very angry one, may decide that it is better to do the former. Otherwise, chains await.
Keran, Act 1
Keran is the last surviving Templar recruit to be abducted. Using either Anders' or Merrill's magic you can determine that he's not possessed, and encourage him to either leave the Templars or vouch for his re-inclusion in the Order. Kicking him out of the Templars means condemning his family to a life of poverty, while getting him back in means potentially revealing Hawke's access to magical assistance (with no consequences, for the time being.)
Ketojan's fate
Ketojan is a Qunari mage, a saarebas, who according to the customs of his people must be bound and restricted at all times. You're asked to lead him out of the city on the assumption that he wants to be free, but you are then confronted by his people who take him back. Hawke can fight to free him, a pro-mage move that pleases Anders among others, or leave him to his people - a potentially diplomatic move with the opposite result. Either way, Ketojan ultimately dies.
Next page: Act 2
