From the sounds of it she's definately fishing about moving back in with you. As far as you asking her to move back in w/you - only you can decide whats best. It just seems all this 'coming around' for her, as far as the dinner/breakfast invite, the phone calls, all coincide with her living situation. I just wonder if she's buttering you up because she needs a place to stay?
I can only speak from the experience of my own situation, and found that my EX would act the same when he was in a tight spot and looking for me to bail him out (which I did too many times) only to be found I was being taken and used. Not a good feeling. While you may have the best intentions for her and the two of you, it may not necessarily be whats best and could very well put you back where you were.
Has she made any changes? Not on the surface, but really put forth some action or has she played the pity card for the most part? I'm not trying to discourage you at all, but you may want to hold off and not rush into it unless you feel 100% sure you can deal with what 'may or may not' come of it.
I know how confusing and painful it can all be so either way I'm wishing you the best of luck.