Question: How do we know which four months are correct?
We learn from the Quran that Hajj shall be observed during the specified Sacred Months (2:197; 9:2, 36). It is also clear from the Quran that the four Sacred Months are continuous, and the Sacred Months and the regular months are not to be alternated (9:37). One of the duties of God's messenger of the Covenant (Rashad Khalifa), was to purge the corruption in this regard, and restore the four sacred months to the ones decreed by God. Please see Religious Duties of Islam (Submission) for the details.
[2:197] Hajj shall be observed in the specified months. Whoever sets out to observe Hajj shall refrain from sexual intercourse, misconduct, and arguments throughout Hajj. Whatever good you do, GOD is fully aware thereof. As you prepare your provisions for the journey, the best provision is righteousness. You shall observe Me, O you who possess intelligence.
(footnote) *2:197 Hajj can be observed any time during the Sacred Months: Zul-Hijjah, Muharram, Safar, and Rabi I. Local governments restrict Hajj to a few days for their own convenience. See 9:37
The four sacred months are Zul-Hijjah, Muharram, Safar, & Rabi` I (12th, 1st, 2nd, 3rd months of the lunar calendar). There is no dispute with Zul-Hijjah being one of the four sacred months. People are comfortable with having Zul-Hijjah as one of the four sacred months as the name of this month itself implies a connection with Hajj. Rabi` is derived from the root word 'Araba' which means 4. There are 2 months in the lunar calendar with Rabi` in their name; the third month of the lunar calendar - Rabi` I and the fourth month - Rabi` II. Use of the word Rabi` (implying 4) for the fourth calendar month is understandable, but why does the third month of the lunar calendar also have the word Rabi` in it? It is fourth of what? It is the fourth of the Sacred Months beginning with Zul-Hijjah.
Furthermore, this is confirmed beyond a doubt in Sura 9, verses 1-5.
[9:1] An ultimatum is herein issued from GOD and His messenger to the idol worshipers who enter into a treaty with you.
[9:2] Therefore, roam the earth freely for four months, and know that you cannot escape from GOD, and that GOD humiliates the disbelievers.
[9:3] A proclamation is herein issued from GOD and His messenger to all the people on the great day of pilgrimage, that GOD has disowned the idol worshipers, and so did His messenger. Thus, if you repent, it would be better for you. But if you turn away, then know that you can never escape from GOD. Promise those who disbelieve a painful retribution.
[9:4] If the idol worshipers sign a peace treaty with you, and do not violate it, nor band together with others against you, you shall fulfill your treaty with them until the expiration date. GOD loves the righteous.
[9:5] Once the Sacred Months are past, (and they refuse to make peace) you may kill the idol worshipers when you encounter them, punish them, and resist every move they make. If they repent and observe the Contact Prayers (Salat) and give the obligatory charity (Zakat), you shall let them go. GOD is Forgiver, Most Merciful.
As you can see, an ultimatum was issued from GOD and His messenger to the idol worshipers on the ‘great day of pilgrimage’ or Hajj. From that moment, they were permitted to roam the earth freely for 4 months. Then, GOD says that once the ‘SACRED MONTHS ARE PASSED’ you may kill the idol worshipers if they haven’t signed a peace treaty with you. Hajj starts in the month of Zul-Hijjah (12), and the sacred months are 4 consecutive months after that. Therefore, Zul-Hijjah, Muharram, Safar, and Rabi I (12th, 1st, 2nd, and 3rd months) are the 4 Sacred Months.
[9:36] The count of months, as far as GOD is concerned, is twelve.* This has been GOD's law, since the day He created the heavens and the earth. Four of them are sacred. This is the perfect religion; you shall not wrong your souls (by fighting) during the Sacred Months. However, you may declare all-out war against the idol worshipers (even during the Sacred Months), when they declare all-out war against you, and know that GOD is on the side of the righteous.
[9:37] Altering the Sacred Months is a sign of excessive disbelief; it augments the straying of those who have disbelieved. They alternate the Sacred Months and the regular months, while preserving the number of months consecrated by GOD. They thus violate what GOD has consecrated. Their evil works are adorned in their eyes. GOD does not guide the disbelieving people.
[5:2] O you who believe, do not violate the rites instituted by GOD, nor the Sacred Months, nor the animals to be offered, nor the garlands marking them, nor the people who head for the Sacred Shrine (Ka`bah) seeking blessings from their Lord and approval. Once you complete the pilgrimage, you may hunt.* ...
We also have a mathematical proof that connects the four Sacred Months with the Hajj verse of 2:197
(sub-title) The Four Months of Hajj (Zul-Hijjah, Muharram, Safar, & Rabi I)
[2:197] Hajj shall be observed in the specified months.* Whoever sets out to observe Hajj shall refrain from sexual intercourse, misconduct, and arguments throughout Hajj. Whatever good you do, GOD is fully aware thereof. As you prepare your provisions for the journey, the best provision is righteousness. You shall observe Me, O you who possess intelligence.
Footnote: *2:197 Hajj can be observed any time during the Sacred Months: Zul-Hijjah, Muharram, Safar, and Rabi I. Local governments restrict Hajj to a few days for their own convenience. See 9:37
The Gematrical Values (GV) of the letters in "Zul-Hijjah" are 700, 6, 1, 30, 8, 3, 5
The GV of the letters in Muharram are 40, 8, 200, 40
The GV of the letters in Safar are 90, 80, 200
The GV of the letters in Rabi` I are 200, 2, 10, 70, 1, 6, 30 700,6,1,30,8,3,5 + 40,8,200,40 + 90,80,200 + 200,2,10,70,1,6,30 + 2 + 197 = 207266732904 =19x10908775416.
If we put all the Suras and verses that deal with the four sacred months and the months of Hajj and the Crescents next to each other they are divisible by 19. 2:189,197; 9:36 concatenated gives 2189197936 = 19 x 115220944
[2:189] They ask you about the phases of the moon! Say, "They provide a timing device for the people, and determine the time of Hajj."
In 9:5 the Quran talks about the four months being skinned from the 12 months of the year. In 36:37 God used the word skinned again to remind us that to skin is to do it in one continuous motion like the change of the night into the day or vice versa. 2:189,197,9:5,36,36:37 = 19 x 11522094492823
[36:37] Another sign for them is the night: we remove (Skin) (naslukho in Arabic) the daylight therefrom, whereupon they are in darkness.
[9:36] The count of months, as far as GOD is concerned, is twelve. This has been GOD's law, since the day He created the heavens and the earth. Four of them are sacred.
Question: Do the restrictions of Hajj apply to all 4 months or only when actually performing the pilgrimage?
Restrictions of Hajj apply only for performing the pilgrimage. With regard to restrictions during the four sacred months, God tells us in 9:36 ... you shall not wrong your souls (by fighting) during the Sacred Months. ... and in 2:217 They ask you about the Sacred Months and fighting therein: say, "Fighting therein is a sacrilege.
Restrictions like misconduct and arguments are applicable for all time as God says in 17:38 - …All bad behavior is condemned by your Lord.
Praise be to God, Lord of the universe.