I would like to ask 4 questions:
1. If someone sights a danger of entering into the state of Ihram, because he will be prevented (a person staying inside Miqaat) how should he assume his Ihram for Hajj? What about a person who comes from outside the Miqaat?
2. Can a Muhrim come outside the state of Ihram before sacrificing and make the sacrifice on 12th or 13th of Dhul-Hajj before sunset?
3. A woman who being ignorant of not knowing that she can assume Ihram, comes to Mecca and waits till she is purified, should she go to Tanim to make Ihram for Umrah so that she could perform Hajj Tamatuu or she also has to give a sacrifice.
4. A family who has resident permit (Iqamah) of Mecca left to Pakistan for vacation, now they want to come and perform Hajj. Should they perform Hajj Tamatuu or can they come inside, stay in Mecca and perform Hajj Ifraad?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

1) If you mean by danger something that could prevent the person from pursuing his Hajj rites, then the answer is that the person is allowed to set a condition at Ihram that his Hajj (state of Ihram) is terminated as soon as he is compelled by necessity to do so (prevented from continuing).  This rule applies at anytime whether the person is still in Miqat hence has just entered the state of Ihram or later on.  Al Bukhari and Muslim reported: Ayisha (Radiya Allahu Anha) said: "The Prophet (Sallallahu Alaihi wa Sallam) visited Dubah Bint al-Zubair and said to her: “Probably you have intended to perform Hajj?” She replied: ‘By Allah I am feeling pain.’  He said, “Perform Hajj and make a condition and say: ‘O Allah my place of Halal (getting out of Ihram) is where You held me up".  

2) There is no objection that the Muslim terminates the state of Ihram before slaughtering the sacrifice.  He/she can slaughter the sacrifice the 12th or 13th.  Al Bukhari and Muslim said: "Allah's Apostle stopped (for a while near the Jimar at Mina) during his last Hajj and the people started asking him questions. A man said, "Ignorantly I got my head shaved before slaughtering." The Prophet replied, "Slaughter (now) and there is no harm in it." Another man said, "Unknowingly I slaughtered the Hadi before doing the Rami." The Prophet said, "Do Rami now and there is no harm in it." So, on that day, when the Prophet was asked about anything (about the ceremonies of Hajj) done before or after (its stated time) his reply was, "Do it (now) and there is no harm."

In fact when you perform any of two of the three following acts you can terminate Ihram and you are allowed to do everything that Ihram prevented except enjoying your wife.  These three acts are: Tawaf, Rami and Halq (shaving).

3) The person who out of ignorance enters Makkah without passing by a Miqat should return to the Miqat and enter in the state of Ihram there and, in this case, does not have to pay any atonement for that mistake.  But if for some reasons, she cannot go back to the Miqat, then she can enter the state of Ihram at Al Taneem but in this case has to slaughter a sheep in atonement.

4) As for the family stated in the question they can perform Hajj in any way they wish i.e Hajj Ifrad, Tamattu or Qiran, if they left Makkah with the intention of returning and residing.  In this case they are not asked to do any atonement as the reason for the obligation of slaughtering for the Mutamatti and the Qarin is that they are not residents of Makkah.

Al Dardiri said, while determining the people who do not have to slaughter for atonement although they are Mutamatti or Qarin: ‘….the person who usually resides in Makkah but left for some lawful reason like business or Jihad and who had the intention to return, is not asked to slaughter a sacrifice in atonement ….’.

But if your question is about whether these people can enter without passing by the Miqat then enter in a state of Ihram in Makkah the answer is that this is unlawful for them and if they do it, their Hajj is correct but they should slaughter a sheep on behalf of each one of them as expiation.