Her note was to hitsugaya and rangiku cos they are staying in her house. How to take care of themselves after she is gone. It's in the begining. Reason she acted like that in front of ichigo is cos she regrets that her life is cut short, final moments with everyone. She has no idea if she'll ever come back to the world of the living or if she'll die or what not. She through her intent can decide if an object will phase through her or not. Which is why she phased through the store Windows and willfully decided to phase through the soccer ball after seeing it. This is mentioned by Ulquiorra. He doesn't want her to tell anyone where she is going since he doesn't want them coming after her or linking the kid nap to Aizen. Yet he wanted to out of courtesy allow her to say her farewell and take care of her business before she left