There are a lot of potential outcomes for Fenris depending on how a series of plot points are handled - and, in one case, whether or not his personal storyline bugs out in Act 2. It's easiest to describe the exact circumstances that create each result. Presuming that you recruit Fenris, he can only die if he becomes rivals with Hawke and Hawke ultimately sides with the mages. Otherwise, he'll either live on with his personal quests unresolved ('Fenris alive but still pursued') or resolved ('Fenris alive and well'). On the off-chance that you feel like being a jerk and handing him back to his Tevinter master, there's an option for that as well.
If you're roleplaying a mage-friendly Hawke who is unwilling to hear the other side of the argument, Fenris' death is likely. Otherwise, 'alive and well' covers a lot of bases. Unless you are a huge jerk, or just like that little picture of him with his top off.
Oh no, Merrill, not again. The adorable elf with terrible ideas can only die if Hawke sides with the Templars at the end of the game and they have a bad relationship. Otherwise, presuming she's recruited, it's quite unlikely that she'll smash the Eluvian mirror (remember those?) that she spends the game slowly repairing. In order to smash it she needs to be Hawke's rival but continue with her personal questline into Act 3, past the point where her former Keeper sacrifices herself to save her. Afterwards she'll regret her obsession and destroy the mirror.
If Hawke is Merrill's friend - even if you don't agree with her actions - she'll keep the mirror, so this all comes down to the nature of that relationship. A hardline Hawke with no tolerance for blood magic or ancient relics would likely not be her friend, but a moderate approach will normally result in an alliance.
Merrill's people can be killed at the conclusion of her Act 3 quest if Hawke chooses certain options when the party leaves the cave where Keeper Marathari was killed. This is one of the worst-implemented decisions in the game, as it really isn't clear which options prompt a fight. If Hawke blames Merrill, the clan lets them go - which is kind of a trap for pro-Merrill players who may be inclined to be more diplomatic.
Killing the clan if you make the wrong decision is forced on you and not presented particularly well, so I'm in favour of going for 'not killed' for this one unless you really intended for your Hawke to take that action - a lot of people will have slipped into it by accident, and that's unsatisfying. A perfect error to fix in Keep.
If you completed Aveline's Act 2 quest and helped her to get closer to guardsman Donnic - one of the game's best plotlines - then their marriage is the result. If Hawke doesn't care for petty things like his companion's personal lives then this probably didn't happen.
Aveline's loyalty is actually fairly hard to lose, so it's likely she'll stick with the Champion at the end of the game. However, if you take a cruel or criminal approach (and try to involve Aveline in it) while also rejecting her requests for assistance then rivalry could lead to her departure at the end.
No real choices to be made here - did you recruit the Prince of Starkhaven or not? Doing so means purchasing the DLC, so many players may have missed him. His involvement is comparatively minor although he does offer a Chantry perspective on certain key events, like when Anders blows up a really old, really kind woman.
Returning from Awakening with a spirit of Justice trapped inside him and a bone to pick with the Templars, Anders ultimately forces conflict between the two sides by blowing up Kirkwall's chantry and everybody inside - with or without Hawke's help. Hawke's role can be oppositional to Anders, supportive of him or deceived by him. Hawke's response, therefore, is fairly nuanced despite the binary options offered. Disapproving of Anders' actions doesn't necessarily mean that Hawke is pro-Templar, after all: the guy blew up a church. Approving of Anders is the more radical stance, because it firmly aligns Hawke with the most hardline elements of the mage rebellion.
Likewise, Anders' ultimate fate may be informed by many different motivations. Killing him outright is the potential choice of a pro-Templar Hawke or a heartbroken mage supporter - or someone who, for whatever reason, really doesn't want to lose Sebastian. On the other hand, sparing him can mean that Hawke wants him to continue his present course or give him a chance to redeem himself - Anders does show regret, after all, and it's possible that their relationship is strong enough for Hawke to want to give him another chance. It's all down to how you want to roleplay it.
Tallis is a temporary companion featured in the Mark of the Assassin DLC. She involves Hawke in a heist on false pretences, ultimately revealing herself to be a Qunari spy on a mission to save innocent lives. 'Not making her angry' means forgiving her duplicity and helping her achieve her original objective; the opposite means you refused to trust her, even if ultimately Hawke still solves the crisis.
It's also possible to romance her over the course of the DLC, which results in a kiss but otherwise doesn't interact with the story (or your other love interests.) Essentially: would Hawke kiss a suspicious elf they'd only just met?
Next page: Prologue and Act 1