The 2nd question: -

> Why is junction capacitance in graphs usually a function of reverse
> voltage and not forward current or something?

The dominant characteristic of a reverse biased diode is capacitance and, the bigger the reverse voltage, the smaller is the capacitance of the terminals. 

When the diode is forward biased the dominant characteristic is forward conduction and this dwarfs the reverse characteristics hence, it makes no sense to try and figure out how junction capacitance varies with forward current.

For the 1st question try reading this: -

![enter image description here][1]

Taken from [here][2]


  [1]: https://i.sstatic.net/UiYHH.png
  [2]: https://books.google.co.uk/books?id=zMVTv6py7woC&pg=PA257&lpg=PA257&dq=dv/dt+failure+mechanism+schottky&source=bl&ots=H3ehEt_P4Y&sig=wHSkbN6aWUSrRawE254nw4iuieA&hl=en&sa=X&ei=OiSXVOGPKOip7AaCvoHoDg&ved=0CDoQ6AEwBA#v=onepage&q=dv%2Fdt%20failure%20mechanism%20schottky&f=false