Welcome to the frustrating, non-intuitive world of the SD skin editor.... On the other hand, it is somewhat easier to edit SD skins, as compared to other front ends.
Couple of answers, although you probably already have the answers, given the date of your questions:
The 'T' button on the top screen has seemed to appear randomly to me as well, although I have never had it appear in the finalized, non-dev environment skin, once I package it for use.
The white outline that is left behind sometimes seems to be some sort of dev environment bug; just save your progress, restart the dev eniornment, and it should be gone.
Undo would be nice, thats for sure!!!
As for editing module screens you don't have, I'm not sure why you can't do that; I have been able to, no problem. I don't have the phone set up yet, but I was able to edit a phone screen