1. Nazr (vow) means making it obligatory upon oneself to do some good act, or to refrain from doing an act which is better not to do, for the sake of, or for the pleasure of Allah.  Thus, it can be done with different intentions. So a vow is the action, on the part of a person who is adult and of sound mind (mukallaf), of obliging himself to do something that is not obligatory, whether he intends to do it straight away or makes his doing it conditional upon something else.
2. When it comes to the offerings you have referred to in your email, we cannot mention anything exactly about their origin because it is very much likely of something to become customary in a certain place due to an incident while other practices might become customary in another place due to other incidents. Hence, such offerings have more to do with customs prevailing in a society rather than any specific religious doctrines.
3. As for the death of some of the enemies of Ahlul-Bayt (as) in the said months, you are requested to refer to index “Nazr of Imam Sadiq (as) in Rajab” question 14640.
4. What has been claimed to be a saying from Imam Sadiq (as) was not found in hadith (textual) sources but it is, generally speaking, one of the desirable Islamic acts to feed and make happy one’s brethren in faith. Imam Baqir (as) says:
«إِنَّ اللَّهَ تَبَارَکَ وَ تَعَالَى یُحِبُّ إِهْرَاقَ الدِّمَاءِ وَ إِطْعَامَ الطَّعَامِ»
“God, the Glorified and Exalted, loves shedding blood (of a sacrifice) and giving of food.”
This Islamic tradition can take place in different ways; it can be in the form of giving food to others or in the form of a nazr (vow) etc.
 Imam Khomeini, Tawzih al-Masail (with annotation), researched and edited by Banu Hashemi Khomeini, Sayyid Muhammad Hussein, vol.2, p. 609, issue 2640, Islamic Publications Office, Qom, eighth edition, 1424 A.H; Vide: Index: Change in Nadhr, question 23041.
 Kulayni, Al-Kafi, researched and edited by Ghaffari Ali Akbar, Akhundi, Muhammad, vol.4, p. 51, Dar al-Kutub al-Islamiyah, Tehran, fourth edition, 1407 A.H.
 Excerpted from Index: The “Feast of Marriage”, question 16227.