Is a rillette typically cooked in fat? I want to know if you have cooked your pork to the point where you can 'pull' it can you further cook the rillette in fat / lard in a similar way to what a confit is done or is the fat just poured over the the cooked pork when you seal the meat in the container?

Can you use pink salt (Nitrates) in your cooking process so as to make the rillette store for many months?
Rillette is pork cooked in fat (not really confit, but close to).

Most of what I've seen on the internets is that you can freeze the rillette for longer storage; if not, keep at most for 30 days in the fridge.

You can pour a little bit of the fat on top of the rillette in the container, mostly for extra flavour, not for long term conservation.

I don't know enough about pink salt (Himalayan salt or the Pink curing salt ?) to help you there.