-Understand handwriting and digitize it?
Yes, that's the whole point of the API.
It's basically OCR 2.0
-Understand Math/Equations and digitize it (ie Latex)?
Nope. Or, at least, not yet because, of course, it would be a logical expansion of the API.
Are there any other APIs that can do this for UWP or Unity?
Not that I had heard of.
Finally, I don't think that Jeans link is what you are looking for. It's not simply a matter of adding a new symbol, but also to represent it conveniently.
For example, how would you do to display \frac{\,\frac{a}{b}\,}{\frac{c}{d}} ?
There is no correct way of positioning the a/b over the fraction bar and the c/d under it. Even if you can use superscript and subscript, there is no way for a standard police to align them vertically.
The good news is: Ink is an API, which means you could create a wrapper that would, for example, automate the latex pdf generation. So yes, you could create the functionality you're looking for with a bit on C# (as it looks you're on a Microsoft environment)
Take a look at this thread: https://tex.stackexchange.com/questions/53914/compile-tex-inside-microsoft-c-net
Best of luck!