In English, "N" is articulated the same way "T" and "D" are - on the alveolar ridge (as all three are nasal alveolar). It seems like in the women's script "N" belongs to a different family from "T" and "D". The former is a "left facing arrow" while the latter two are "right facing arrows", to use some very basic description of the symbol shapes. Why is that?
Peter might have a better explanation for this, but because of the three sizes, we had to group things in ways that didn't always make sense. The N was a fourth letter in a set (TDL), so looking back, maybe we should've grouped N with TD instead of the L, but then that has a cascading effect, so this was the best we could do in the time we had. But we don't know exactly how the Alethi speak. There's always a chance that the Alethi Z sounds more like "dz," and the Alethi "S" sounds more like "ts" (like the German Z), in which case the SZN grouping makes a lot more sense. But that's just conjecture.
The symbol sets are all based on historical place of articulation (and articulating tongue part), and there have been some sound changes over the centuries so they don't currently all line up exactly. The t/d/r/th/l group (historically alveolar) is articulated with the tip of the tongue, and the s/z/n/sh/h group (historically postalveolar) is/was articulated with the blade of the tongue.
The modern h sound (like h in English) used to appear only in the palindromic locations, and was written only with the diacritic. This diacritic is mirrored on the top and bottom of the character. Some writers may use only the top or bottom because lazy. Also, sometimes the diacritic can be left out entirely and people just know to pronounce it as h because it's a very common word or name.
The h character used to stand for a weakly-voiced postalveolar non-sibilant fricative. This later shifted backward to a velar fricative (first weakly-voiced, later voiceless) as in Kholin. In modern times the h character is usually for the same h sound that we have in English. Sometimes kh is written using a combination of the k and h characters, and sometimes it's written just as h for historical reasons. Different regional dialects also shift the pronunciation one way or another.
The L sound has also shifted. It used to be a voiced alveolar lateral fricative, and this is still seen in names like Lhan. It's now a regular L sound.
The final group, k/g/y/ch/j, used to have dual articulation, similar to velarized postalveolar. Now the articulation has separated, with some velar and some postalveolar.
Currently y and j are pronounced the same or differently based on class and regional dialect. So, a darkeyes name like Jost or Jest will be pronounced with a regular j sound, while with the upper class it has merged with y so that Jasnah and Jezerezeh are pronounced with a y sound. Historically they were always separate sounds.