Let's deal with these questions:
- Who were the Shunammites? These are dwellers in the city of Shunem located about 3 miles (5 km) N of Jezreel, near Mt. Gilboa. When the land was divided in the days of Joshua, Shunem was given to the tribe of Issachar (Joshua 19:17-23). So, the Shunammites are Israelites of the tribe of Issachar although it remains unclear if the original inhabitants were destroyed or whether there was a mixing of Israelites and Caananites in that area. Shunem means Uneven and perhaps got its name because it was situated on a hillside overlooking the Jezreel valley. Some commentators feel that it was from Shunem that the bride came in Song of Solomon 6:13.
- Why was the woman not mentioned by name? That is unclear although her association (at least in terms of place) with the bride in Song of Solomon may mean that, unnamed, she is an apt representative of the bride of Christ. She was a woman of some wealth and stature but faithful. She is to be contrasted to another great woman, that paragon of evil, her contemporary, Jezebel.
- She was intent on seeing Elisha. The phrase it is well is the simple Hebrew greeting, Shalom. She gives a peremptory response to Gehazi who seems to be attempting to intervene and prevent her from going directly to Elisha. In response to his queries, she in effect says, yes, yes, yes or Shalom, shalom, shalom and she probably didn't slow down as she spoke. Is there something we can learn about our approach to the Lord and the sometimes unnecessary and perhaps self-serving attempts at mediation by means of a clergyman? Just a thought. Gehazi's anger indicates that he did not appreciate her direct approach to Elisha. There are times in the NT when the Lord's disciples acted a bit like Gehazi. I'm sure those same examples have come to your mind.
- Regarding the staff: That is an interesting question and the only answers we can provide are pure conjecture but, perhaps, not unreasonable even so. Perhaps Gehazi was sent ahead because he was younger and more fit than Elisha with the staff being a surrogate for the prophet. Did Elisha wish to show his servant that his heart was not right? Was he trying to dissuade the populace from a belief that a thing such as a staff could have, in and of itself, magical powers? Or was Elisha as amazed as Gahazi was disappointed that God would not work such a miracle through his flawed servant? I think the latter is the case. I don't think Elisha would have sent Gehazi on the mission if he knew in advance that it would fail. In any case, the woman knew better. She knew that only Elisha could save her son. She had taken Gehazi's measure even if the prophet had not yet done so. Gehazi was weighed in the balances and found wanting.
- Gehazi went on ahead but the woman would not leave Elisha and while the servant ran on ahead in his ineffectual mission, she stayed with the man of God. She said, As the LORD liveth, and as thy soul liveth, I will not leave thee. (cp. Matthew 15:21-28). Such faith demanded only one response, Elisha rose and returned with the woman to her home. She knew that no one else could bring life to the dead. What a lesson for us This woman had received a prophet in the name of a prophet and had received a prophet's reward. In this case it was life from the dead. She had rejected false mediators and talismans and focused all her hopes on the man of God, Elisha - short for Elishua God is salvation.
- Death still reigns in God's creation. It is the last enemy to be destroyed in the Kingdom Age (1 Corinthians 15:26). Though death still reigns, we sorrow not as others do. For, though the dead know not anything (Ecclesiastes 9:5-10; Psalm 146:3,4), one day they shall hear the voice of the man of God calling them back from the sleep of death. Those that hear shall live indeed
It is interesting to note the almost exact parallel with Elijah and the widow of Nain in 2 Kings 7:8-24. Is the anonymity of these women an undesigned scriptural coincidence showing that these chronicles were written very close to the time of their occurrence? It would have been a very risky thing to do to shelter either prophet as they were considered enemies of the state at the time. Therefore it would have been unwise to name them lest the authorities react badly to their Godly act of hospitality.