The word "shaf'" literally means adding something to something else. It also means "even" as opposed to odd. The Quranic verse says "wash-shaf'a wal-watr" in which "shaf' means even while "watr" means "one".[1] " Shafa'ah" (intercession) is derived from "shaf'" which means adding something to something else.[2]
The reason this prayer is called "shaf'" is because it consists of two rak'ats. Some exegetes have said in the interpretation of the following verse:
«مَنْ یَشْفَعْ شَفاعَةً حَسَنَةً یَکُنْ لَهُ نَصِیبٌ مِنْها وَ مَنْ یَشْفَعْ شَفاعَةً سَیِّئَةً یَکُنْ لَهُ کِفْلٌ مِنْها وَ کانَ اللَّهُ عَلى کُلِّ شَیْءٍ مُقِیتاً»[3]
" Shafa'ah" (intercession) is derived from "shaf'" which means "even" as opposed to odd - the interceder adds his own recommendation to the plea of the petitioner; in this way the number of pleaders becomes even, and the weak plea of the petitioner is strengthened by the prestige of the intercessor.[4]
As for the last part of the question, we must say: Well-being and good health are the fruits of the night prayer as stated in some traditions. For further information about them, you are advised to study the following indexes:
"The Importance and Effects of the Night Prayer and the Rules regarding Its Qaza", question 60928.
"Night Prayer", question 60929
[1] Vide: Difference between "even" and "shaf'", question 37518.
[2] Waseti Zubaidi, Sayyed Muhammad Murtadha, Taaj al-Aroos min Jawaher al-Qamus, researched and edited Shiri, Ali, vol.11, p. 250, Beirut, Dar al-Fikr for Printing and Publication and Distribution, first edition, 1414 A.H.
[3] Nisa (4): 85: "Whoever recommends and helps a good cause becomes a partner therein: And whoever recommends and helps an evil cause, shares in its burden: And Allah hath power over all things."
[4] Tabarsi, Fadhl bin Hasan, Majma'ul Bayan fi Tafsir al-Qur'an, preface, Balaghi, Muhammad Jawad, vol.3, p. 128 – 129, Tehran, Nasir Khosro Publications, third edition, 1372 (solar)
source : islamquest