A simple arrow on the grid pointing which direction is forward.
A lot of us have asked for this. It'd be nice.
Also on the grid, mark the boundaries of a Large, Medium and Small ship size.
This is not necessary; the game will do it for you.

I did a little experimenting: these are the exact same ships with the exact same weapons and engines; the only difference is which size I chose. The game will scale it for you based on which you picked.
Let us copy parts that have already been placed.
Agreed. An eye-dropper or copy/cut/paste tools would be handy.
Simple Objects!
Again, agreed. Some sort of null object to use as a base object would be handy.
Different tabs to separate the objects in categories. I kept getting lost trying to re-find a certain object I placed.
On the one hand, yes, because I often lose my place, too. But on the other...with only a few exceptions--like engine parts that will generate a stream while in battle--parts are used only for what we decide. Goodness knows that there are a few with which I've done some rather odd--and certainly unintended--things.
Let us manually type in numbers!
On the one hand, yes, that'd be nice. But on the other, it's clear when looking that every number is a snap point; even the bits that look like decimal places will always end up at the same value every time.
Without a copy-paste tool for item values, I'm not sure typing in numbers is the best idea.
Trying to get that exact 90 rotation is a pain.
Which is obviously why 90 is one of the snap-to-values; it really shouldn't be a pain at all.
Not that I don't share your sentiment that it'd be nice to have a few short-cut buttons. But still...