And your question is...
I'm not quite sure what the exact thrust of your intended question is. It seems to be about how to go about making the concept of a merfolk more realistic? And also if your existing suggestions are realistic?
Assuming that is the case:
Point one: Tail movement
It will be noticed that, most, if not all ocean mammals move their tails up and down, not side to side, while non-mammalian fishes again most, if not all, move their tails side to side. As such, it only makes biological sense for a mer to move their tail up and down, as they are (being half "human") presumably mammalian.
It is indeed odd that mer tend to be called out specifically as "half-fish". Perhaps this notation stems from taxonomically ignorant origins, people who in their time and era called anything and everything that swam in the ocean a "fish" and were not aware of the differences between mammalian and non-mammalian ocean creatures. (Not to mention that mythology does not always make sense, even if there was awareness of the differences back then.) As such, there should be no issues with, and indeed should likely be more genetically possible to have mer be half-human and half-mammalian ocean creature instead.
Point two: Hair
Hair is ascetically pleasing to a human, but seems rather unnecessary in an amphibian or purely water-breathing species. As pointed out, it would produce drag, and seemingly serves no other purpose than the ascetic.
Here, the origin would become critical. If the mer are augmented or altered creatures using humans as a base, and if the initial tweaking did not remove the hair, then the mer would still have hair from their human heritage, useless as it may be.
It would seem quite the disadvantage to have hair underwater, unless it was replaced with some sort of sensory boosting appendages that superficially resemble hair and are less drag-producing that traditional hair. Of course, if they are amphibious, and not purely water breathers, then perhaps the hair would be left in place for their above-water times. The above-suggested short-length hair would seems a more viable option in such cases. Another option is to replace the hair with an analogue, fins or some other mechanism for display or ascetics.
Given the mythical stories and origins of the mer: namely, that they were a species that hunted men specifically, luring them to death and/or doom, it actually makes sense for them to have hair for those purposes, noting again that hair is considered attractive to humans.
For a realistic and viable race of mer, with both male and female, and assuming that they don't need to hunt human males for some reason (such as an all female race or something) then it would make more sense for them to not have hair - barring the above mentioned [possibility of sensory appendages. Another slightly more far fetched justification for hair would be harvesting and using hair as a tool - weaving it into water resistant fabrics and ropes. Given that forging is going to be problematic underwater, tool development and usage will be somewhat more challenging.
Point Three: Nose
This will again depend upon amphibious versus pure water-breathing. In either case (and I was going to suggest chest-gills myself, but I see that it was covered in the question referenced) the nose would likely be streamlined and on the small end of the spectrum for the amphibious mer, if not flattened or removed entirely for a pure water-breathing mer.
Given the comments about oxygenation, it would seem the amphibious version would have more potential realism.
Point Four: Senses - Visual and Auditory
Visual adaptations for low light would seem critical given that so much of the ocean is little to no light whatsoever. Also, a nictitating membrane would seem critical for eye protection (given the amount of debris floating around).
However, more of the ocean is dark than lit. Fortunately, human echolocation is a real thing, with the more extremely talented examples being able to walk or bike around town, skateboard, even playing video games(!) solely using echolocation. (Ben Underwood and Daniel Kish are a couple of the more famous examples.) For an ocean-going (amphibious or not) creature, it would seem that honing and developing this ability would become critical for navigation and creature recognition, and perhaps some more robust vocal cords might be in order.
I imagine that singing, above or below water, could become the mate attraction of choice. Recall also the possible hair analogue suggested previously for display purposes.
Point Five: Coloration and Skin
Depending on the target dwelling and intended travel regions and areas, the skin becomes quite important. A shallows dwelling creature will have different composition to the skin than a more widely-ranging ocean-going type, notably, the fatty tissues directly underneath the skin.
An ocean-going type mer would need to be able to withstand the cold and potentially the crushing depths of the oceans, needing a much thicker layer of blubber, and some other internal structural differences for long / deep cruising. Especially the deep dives.
Having a coloration and body shape that can blend in with or mimic other creatures would be a potential advantage in cohabiting and/or cooperating with native ocean creatures, as well as times when hiding amongst the crowd has benefit. On the other hand, it could also get them mistaken for valid prey by certain creatures.
A chromatophoric integument would have certain advantages as well. Not only could mer pull off the above mentioned tactics, they could also hide against objects and the sea bottom. In areas with light, it could also serve as a non-auditory form of communication. Combine with the optional ability to fluoresce, and you have signalling capabilities even in the depths. (And a possible method to lure prey (or mates) to themselves!)
Finally, in a natural or survivability-designed mer race, streamlined skin would be the ideal and most advantageous, as such while the chest cavity would likely be rather large (see oxygenation comment above), female mer would tend towards (ahem) smaller mammalian organs. Anything else would produce considerable drag during water maneuvers. I will decline to comment on mer designed for purposes other than survival.
Most of the comments and suggestions made in the original question seem to on the whole support the survival and prosperity of an amphibious race of mer. I hope my additions are helpful.