I am by no means a Nami main, but I have played her quite a bit this season (I am a Janna main, but Nami has been my secondary highest champion in ranked this season -> here for op.gg) and the question of Ardent Censor is quite a common one. In my personal experience, most of the time, the only people I really find it good building for is if you have two auto attackers (Not casters like Jhin, Corki) preferably your ADC (the only ones I usually build it for are Kog'Maw and maybe Draven, but I'll get into that later) and jungle/top (For example, Xin Zhao). However, most of the time I find that the item is more of a "fun" item and there are usually better things you can do with that gold. For example, Mikael's Crucible is only 100g more but the active (even though it had a long CD) is generally fight changing in a lane or teamfight. It gives Nami most of what she wants (mana regen, CDR, some MR) while sacrificing a few combat stats in favor of a QSS + Burst heal. It also delays a lot of items that most babysitter supports should build (Mikaels, their upgraded GP10 item, Banner/Locket, Frozen Heart/Randuins, Boots) unless you're going straight AP in which case, Ardent probably shouldn't be on your "to build" list either way imo.
Another issue I have with building Ardent Censor is that most of the time, you end up roaming by the time you have enough gold for that. Dragon becomes an objective, mid becomes the focus (unless it's literally just a Farm Simulator game) in which case I find it a lot more useful to just build a Locket/Banner if the mid laner is fed, or a Frozen Heart even if there's a fed bruiser on the enemy team (Xin, Shyv, etc), or like I mentioned before, Mikaels. My theory about Ardent Censor is that yes, it does give the "Magic Damage on hit", however, if your ADC is dead due to getting caught by CC, they won't be able to pump out damage anyway. As for the AP that the item gives, I would say that you're better off buying Banner of Command if you really want the AP since it's generally more useful for your team overall by providing MR (considering how most mid laners are either caster ADCS and Control Mages that don't really want to AA).
Anyway, tl;dr
Ardent Censor is a fun item to buy, but overall I find Mikael's Crucible's active a lot more game changing in most cases than the little "oomph" Censor adds to your ADC. If you're going to buy it for any champion, buy it for Kog'Maw, but only if you're sure that Koggles can survive the enemy team and generally won't be in a situation where he can be caught by CC/bursted. For other adcs, while it may boost them a little bit (i.e. Dravens that have a lead), you're generally better off just building Mikaels/Aegis item in order to keep them alive.
Regarding the Exposed Weakness mastery, I personally find that the Ferocity tree just doesn't provide enough for it to be worth it. Generally early laning phase the 2 damage reduction from Tough Skin as well as the bonus health from Veteran Scars have a HUGE impact on lane since it allows trades especially for someone as squishy as Nami and the SS reduction is always nice. However, it's personal preference since I do not build that much AP on Nami for Sorcery to become useful enough to be worth it.