Doing Wudu and Ghusl While Wearing Fixed Wig
Question

I am a twenty-seven-year-old woman. I am completely bald on my head as a result of sickness, may Allah grant us and you wellbeing. This causes me a great deal of embarrassment when I have to meet people, and in front of my colleagues at work. That has had a great impact on my psychology. It was suggested to me that I could replace my hair with a wig that is attached to the head and remains there, and can be taken off the head once a month. Is it permissible for me to wear this type of wig, and to do ghusl and wudu and pray whilst wearing it? This is the most appropriate for me, as the nature of my work and my life requires me to be with people all the time, and I find it very difficult and embarrassing to conceal this defect. Please advise me urgently, as  I am in a great deal of emotional distress.
Praise be to Allah.Can Muslim women wear  wigs?
The basic principle is that it is haram to wear a wig because of the report narrated by al-Bukhari (5477) and Muslim (2127) from Humayd ibn ‘Abd ar-Rahman ibn ‘Awf that he heard Mu‘awiyah ibn Abi Sufyan, during the season of Hajj, saying on the minbar – taking a hairpiece from his guard’s hand –: Where are your scholars? I heard the Messenger of Allah (blessings and peace of Allah upon him) forbid things such as this, and he said: “The Children of Israel were doomed when their women adopted such things.”
Many of the scholars regarded wearing a wig as coming under the same heading as adding hair extensions, and Allah has cursed the woman who adds hair extensions and the woman who asks to have them added, as al-Bukhari (59937) and Muslim (2122) narrated from Ibn ‘Umar (may Allah be pleased with him) that the Messenger of Allah (blessings and peace of Allah be upon him) said: “Allah has cursed the one who adds hair extensions and the one who has them added, and the one who does tattoos and the one who has them done.” (See Fatawa al-Lajnah ad-Daimah, 5/191)
Some of the scholars are of the view that there is a concession allowing a woman to wear a wig if all of her hair has fallen out.
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) was asked about a woman who took medicine which led to the hair on her head, or most of it, falling out, and she does not want to use a wig because she thinks it is haram. He replied:
“With regard to using a wig in a case such as the one you described, where her hair has fallen out in such a way that there is no hope that it will grow back, we say: in a case such as this, there is nothing wrong with wearing a wig, because in fact it is not for the purpose of enhancing beautification; rather it is in order to remove a defect. Based on that, it does not come under the heading of adding hair extensions, for which the Prophet (blessings and peace of Allah upon him) cursed the one who does that, as he cursed the woman who adds hair extensions and the woman who asks for them to be added. The one who adds hair extensions is the one who attaches something to her hair. But in fact, this woman does not come under the heading of hair extensions, because she does not want to enhance her beauty herself or add to her natural hair that Allah, may He be blessed and exalted, created; rather she wants to remove a defect that has occurred, and there is nothing wrong with that, because it comes under the heading of removing a defect and not under the heading of enhancing beautification. There is a difference between the two matters.” (From the Shaykh’s website)
And he (may Allah have mercy on him) said: 
“If someone were to say: What do you say about a bald woman who has no hair on her head – is it permissible for her to wear a wig to cover the defect, not for the purpose of enhancing beautification or making the hair longer?
The answer – and Allah knows best – is that it is permissible, but there is the story of the woman and her daughter who caught the measles and her hair became thin. She asked the Prophet whether she could add hair extensions and he did not allow her to do that.
The response to that is: what appears to be the case is that the hair was not lost completely, hence she asked to be allowed to add hair extensions, and asking to add hair extensions indicates that  some of the hair was still present, and if some of the hair is present, then adding to it is done for the purpose of enhancing beautification. But if there is no hair, then it is a defect – what I mean is that her head looks like her cheek, with no hair on it at all. And this is something that happens. Do not think that this is a hypothetical matter, for it is not a hypothetical; rather it is real. In that case it seems to me that there is nothing wrong with this, because the purpose is different from the purpose of adding hair extensions, which are not allowed, or it was narrated that the doer is cursed, and that is what is referred to in the hadith.” (Sharh Sahih al-Bukhari, 7/599, 600)
Ruling on hair implants for one whose hair has fallen out
It is permissible for the one whose hair has fallen out to seek a remedy, even by having a hair transplant , and this does not come under the heading of changing the creation of Allah; rather it is a treatment to restore what Allah, may He be exalted, had created.
It says in a statement of the Islamic Fiqh Council of the Organisation of Islamic Cooperation that was held during its eighteenth session in Malaysia 24-29 Jumada al-Akhirah 1428 AH/9-14 July 2007 CE, regarding cosmetic procedures and what is permissible thereof: 
“Correcting acquired defects that result from burns, accidents, disease and so on, such as skin transplants and patching, reshaping of the breast completely in the event that it has been entirely removed, or partially reshaping it if its size is too large or too small, such as if it may lead to health problems, and hair transplants in the event of hair loss, especially in women.”
How should one who wears a wig do wudu and ghusl?
If you wear a wig, you may wipe over it when doing wudu , because the concession allowing wiping over it is based on making things easier, and because the Prophet (blessings and peace of Allah be upon him) stuck his hair together in a process called talbeed when doing Hajj, and wiped over it, meaning that he put something like glue over it, to hold the hair together and not let dust get into it.
However it must be taken off when doing ghusl, because it is obligatory to make the water reach all of the skin.
Can women appear in front of men wearing the wig? 
It is not permissible to appear in front of men wearing the wig, because it is a kind of adornment that must be covered, in addition to what it may involve of attracting men’s attention.
We ask Allah to grant you healing and well-being.
And Allah knows best.