I like your post, Phaz but I also disagree with some of it.
So, Inquisitors. We know that they can be made from allomancers (Marsh). We know that they have the powers of a mistborn. We know that their abilities are usually stronger than normal Mistborn. We know that they use allomancy.
We do not actually know that they have the powers of a mistborn, at least from what I recall. If you have a passage to support this, I would appreciate it. As is, we know that they can push/pull metals and that they can use atium. It is likely that they strengthen themselves with pewter. However, I can't recall an inquisitor ever using emotional allomancy. They would have no need of tin as it would not help their "blue line" vision anyway, and hearing better wouldn't really help them. They don't need aluminum, and likely not duralumin as they are so powerful in the first place. I would say that it is possible that they have the powers of mistborn, but has by no means been proven.
I don't have a ton of time, but wanted to address this quick point.
First, it's true, we haven't seen them use all the powers of a Mistborn, but IMO they have been shown (or we've heard) about them using many. I'd say we know they can use steel, iron, atium, pewter, bronze, and possibly copper.
They don't need to have
all the powers of a Mistborn, especially if we are assuming that hemalurgy simply 'steals' the power of a misting. Why take something you aren't going to need? They won't need Tin to see, but could perhaps use it to hear. The emotional ones probably aren't necessary though, nor is alumninum, so why bother?
As for the rest. I would say that what we see inquisitors do is the same as what we see allomancers do. My best evidence for this are two key fights.
When Kell fights the inquisitor, the fight seems very balanced. They are both strong in the same way, they both use metal in the same way, they both move in the same way. I can't point out a lot of specific details, but it has the 'feel' of them being very much the same.
However, when Sazed fights Marsh, the fight does not feel that way. Sazed can move much faster than Marsh (for short periods). When Sazed changes physically, he
changes physically. He gets inhumanly large or or thin or muscular.
To me, reading about inquisitors, it just seemed like they were using the same powers. They do things in the same way.
Also, we know metal is involved, so maybe the different types of metals are what effects what abilities you can steal. Such as maybe a gold spike will steal the healing ability from a feruchemist, and a different kind of spike would steal a different ability.
Finally, feel free to be as critical of my posts as you can
I believe it was Einstein who was famous for pointing out that no number of people agreeing with you can ever make you right. However, it only takes one person to prove you wrong.