I think the standard response about Merrill in game is that whether a friend/rival/romance she is in Kirkwall helping the alienage elves. If a rival she destroyed her eluvian so it is no longer an issue. If a friend it was still inactive at the end of DA2. May be she was persuaded to shift it off somewhere between then and DAI for safekeeping, so wasn't aware that it became active either through Briala's actions or Solas taking back control. Certainly by the end of Trespasser Solas apparently now controls the whole network, so I would imagine that every eluvian he is not immediately using would be de-activated to ensure that no one unauthorised enters the network. The eluvians as a plotline are still very much active since they are controlled by the current main enemy of Thedas.
The sacred ashes weren't destroyed by the Conclave; I'm pretty sure I remember a codex that says they were removed by the Guardian and taken off to an undisclosed location. I doubt they will feature again because basically they have done their purpose in the first game and Haven was destroyed along with the mountain in the course of DAI. I suppose it is just possibly that the Guardian might turn up with the ashes to heal/restore a hero from the dead as part of a future plot but on the whole I doubt it.
Abominations weren't really a big feature of DAI because demons were able to get into the world without the need of an in world vessel. The whole Grey Warden plot centred around the fact that Corypheus wanted a demon army to work for him, so any demons with ideas of world domination already had someone working on their behalf. The problem was that not having mages go "poof" and turn into abominations at the drop of a hat was such a stark contrast to DA2. Instead we just had people like Vivienne emphasising the need for vigilance because of the danger. Mind you blood magic had disappeared almost completely as well, even among the Venatori where you would think there would be any number of master practitioners. The risks associated with blood magic were centred around the fact that it left you open to a greater chance of being possessed because of the attraction demons have to the shedding of blood (never really explained to date) but Last Flight makes it clear that all mages are at risk and can feel demons at the edge of their consciousness even when simply casting ordinary spells because of the connection this makes between their mind and the Fade. Grey Warden mages that are cut off by darkspawn in a hopeless position had been known to allow themselves to be possessed at the end simply in order to take out as many darkspawn as possible before they die. Dorian did say that killing yourself and everyone else just to avenge yourself against your conqueror was "thinking like a blood mage", so now the Breach has been closed and we are moving to Tevinter, I think there is a good chance that abominations may make a renewed appearance.
Most other people/plots shown in the original post were minor compared with the overall scheme of things, particularly now we are heading north:
Avernus and his research are mentioned in the Keep and the HoF was looking for a cure, so it may be brought up again at some point, particularly considering the link that is being hinted at between Mythal, the Titans and the Blight.
The Architect may be dead (although Cory would seem to disprove this action on the part of the Warden) but could still play a part in future plots. It was odd that he was never mentioned in DAI in connection with Corypheus or even by him, but may be the Architect was simply biding his time and watching developments.
Oghran, Sigrun and Velanna are not really important enough characters and have various outcomes in Awakening, so probably best left. If they can ignore the creation of the Silver Order by my Warden, then they can ignore them too.
Kal Sharok is far more likely to feature in future games than Orzammar, so the outcome of the election of the king will probably only feature as part of conversation rather than play any important part in the plot.
Shale may turn up. In one version of the end of DAO Wynne was meant to be travelling to Tevinter with Shale. However, based off Asunder, it would seem Wynne got too embroiled in Circle politics and that particular mission was put on hold. So following Wynne's death Shale may have headed north..
Connor is a minor character who may or may not have been dead at the end of DAO. If alive, he is seen in Redcliffe. I would imagine that if you do the mage path, he returns to live with his family, at least until the Circles are restored (if they are). Probably does well under whichever person is made Divine. If you do the Templar path then he is dead.
I hope we never see Harvesters again. I have never done the DLC but fighting Orsino was one of the most tedious and boring fights I have ever been forced to take part in. At least other boring adversaries have the good grace to die quickly.
As someone else has mentioned, if Alistair and Warden jointly rule, then he is still doing so, whilst the Warden is off looking for a cure.
The cure is something of an unresolved plot, particularly since a Warden in a romance with Leliana returns to live with her, without any indication of whether or not a cure was found. However, it ties in with the comments of Avernus and likely the cure plot, if not the Warden, is something that will crop up in future.