Some translations read a wealthy woman, others a great and others a woman fearing sin. The last would make her greater than wealth.
She recognized Elisha as God's man and wanted him to be welcome in her home. An interesting concept, is God welcome in our homes? She went so far as to provide an actual guest room just for Elisha. I don't think that's necessary but I'm reminded of the movie The War Room, a closet converted into a prayer room. Not a bad idea. Elisha takes compassion on this woman, wanting to do something in return. His first suggestions deal with his personal influence, able to associate with the powerful people. But this woman doesn't seem to care about that. The servant Gehazi makes the suggestion, and again it must be stressed that although Elisha speaks the prophecy of her having a child, the power and promise came from God and not Elisha. He is a man just like any other man and has no power of his own. We're not told of what conversations he has with God. Perhaps he prayed and God told him, whatever you decide to give her I will provide. In any case what she wanted most was a son and God gave her one.