Is there a way to set a new point for you to begin looking at when you go into one of your own cells to edit it? I somehow managed to start making my structure above and behind the default one, and ever though it's not that hard to turn all around and find a piece of it to click on and 'jump' up to, doing every time is getting annoying.

No, but any object ID you double click on in the cell's object window will teleport you to it.
So you can use this before even loading the cell, instead of just entering the cell in general. (or for teleporting around the cell)

Oh ok. Thanks. Huh. Should have thought of that.