I can see why some might class the friend as a closet ISTJ, since she is exuding a coldness that is usually more indicative of T than F, but I do not know enough of her past and present life situation to make a confident statement. Depending on the stresses that they have lived under, ISFJs can easily become cold and cynical and bitter.
She is probably being nosy as well. That's a problem -- it is usually a mix of good and bad.
If you feel like letting the cork ricochet out, you can just set some boundaries for her. They might upset her; they might also keep her out of your face, though. The more concrete the boundaries, the better; asking her to decide on her own every day what an appropriate level of contact is will confuse her and not satisfy you. ISFJ women very much seem to appreciate definitive statements of what please other people and what does not please them, so they can accommodate if possible.