What's the name of the part the tie rod end screws onto?

And is that part replacable (It looks like it going into the steering box?)?

Also - does my diagnosis from the picture look accurate about the piece that was bent?

That's the inner tie-rod end which connects to the steering rack.
It looks bent!
You can replace it.

Would your guess be that the tie rod end itself is bent, or the piece it threads on to - Which goes straight to the steering rack????

//edit
Typed this before you edited

The inner tie rod end is just a rod that goes between the outer tie rod end and the steering rack.
One side of the rod has a ball joint which threads into the rack.
The other side is threaded to accept the outer tie rod end (this is the shaft that appears to be bent).

I've only had this replaced at a shop, but I watched them do it.
- The length between the rack and the outer tie rod end (where it sits on the inner end) is measured so that alignment can hopefully be retained.
- The outer tie rod end is removed.
- A special cylander that resembles an extremely deep impact socket is slipped over the inner tie rod end. It has a hex at the rack end (to turn the tie rod end out of the rack), and a slot for a 1/4" drive impact gun at the other end.
- The old tie rod is removed with this tool and the new one is installed.
- The outer tie rod end is reinstalled to the measured distance from the rack.

I'm not sure how this would be done without the special tool.

You may have to do an alignment afterwords.
The rod is bent and so it could be difficult to measure with any accuracy.

Is it a one hour job for a shop with the tools?

So basically the outer tie rod end screws into the inner tie rod (Which is the bent piece), and the inner tie rod connects to the steering rack via special joint?

And it's possibly that the ball joint at the steering rack would be messed up from hitting the curb this hard?

That "ball joint" (for lack of a better term) is actually a component of the inner tie rod end.
You'll end up with a new one.
If I were you, I'd be replacing (or at least checking) the outer tie rod end as well, since it also has a ball joint of its own.

As I recall it is one hour on the books.