Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.

A woman does not need to observe Hijab in the privacy of her home as long as she can be safe from gouging eyes.

If as you mentioned the strangers can see the women going around without hijab, then she needs to guard herself; she may have to use a screen where others cannot see her.

As for hijab or modest attire she ought to wear in front of non-mahram who visits her home, she is required to cover her body except her face and hands:

The prophet told Asma’ who was his sister-in-law – sister of his wife `A’isha; when she appeared before him in a less modest attire: “O Asma’, when a woman reaches maturity nothing of her body should be exposed to strangers except her face and hands.”

So, if this rule applies to Asma’, in front of the Prophet who was his sister in-law, then the same should apply to others as well.

As for the rest of your question, let me cite here one of my earlier answers:

Islamic rules of Satr (covering) for women are intended to safeguard and preserve the honor and dignity of women. Rules of covering vary according to whether the degree of risk of seduction/temptation is greater or lesser; where such risks of seduction/temptation are greater, rules of covering are stricter, and where the risk is minimal, rules are minimal.

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Rules of covering are, therefore, stricter in the presence of males who are strangers ( who are not related to her by blood, marriage or milk-relationship). All scholars agree she must cover her entire body except her face and hands.

As for males who are considered maharim (those who are related to her through blood, marriage or milk-relationship, and whom she can never marry) all scholars agree that she does not need to observe the above strict rules of covering; rather all of them agree that she is allowed to uncover her hair, face, hands, neck, feet and shoulders in front of such relations.

Coming to the question of what she must cover in presence of women, some scholars make a distinction between Muslim women and non-Muslim as regards the degree of covering.

There is general agreement among scholars that she may uncover her hair, face, hands, neck, shoulders, legs from below her knees as well as feet in front of Muslim women.

Concerning what she must cover in presence of non-Muslim women, broadly speaking, there are two views, one may be considered very liberal while the other may be considered very strict. Both scholars of the Maliki and the Hanbali schools generally consider only what is between navel and knee as the awrah that a woman ought to cover as a must in front of other women, regardless of whether they are Muslims or non-Muslims.

As opposed to the above view, both the Hanafi and the Shafi scholars consider it obligatory for her to cover her entire body except what is normally exposed in ordinary course of daily interaction and domestic work. They consider it a must for her to cover all her body except her face, hands and feet.

The above difference of opinion is based on the differences in interpreting the Qur’anic verse concerning rules of covering “they shall not display their charm except what is apparent from it in front of…..or their womenfolk” (An-Nur 24:31). According to the scholars of both the Maliki and the Hanbali schools, the phrase “their women” includes all women including non-Muslims, while the scholars of both the Hanafi and the Shafi schools say rather it specifically distinguishes Muslim women from others, and, therefore, she must observe stricter rules of covering when appearing before non-Muslim women as opposed to Muslim women.

The last mentioned view that a Muslim woman is absolutely obliged to cover her entire body except her face, hands, and feet in presence of non-Muslim women seems to be a little extreme. We find no evidence in the sources to support such a conclusion; there are numerous instances of non-Muslim women, from both Jewish and pagan backgrounds, visiting the wives of the Prophet, peace be upon him, as well as other Muslim women, and yet, there is no mention anywhere that the Prophet, peace be upon him, ever ordered them to observe special rules of covering in their presence. If it had been necessary for them to do so, it is most unlikely that the Prophet, peace be upon him, would have failed to mention it to them plainly and clearly.

Therefore, the view of Maliki and Hanbali schools on this issue seems to be more consistent with the evidences of the sources, as well as the general spirit of the Shari’ah.

Having said this, however, it must be stated clearly: All scholars agree that while normal laws apply in normal circumstances, where there is a suspicion of seduction or temptation or inclination towards vices either due to corruption of society or moral perversion, Muslim women are obliged to take all necessary precautions and thus cover appropriately in order to safeguard their honor, dignity and chastity.”

Almighty Allah knows best.