Question: What is the ruling regarding cutting the hair for women? If it is allowed, then how short can she cut it?

In the name of Allah, Most Compassionate, Most Merciful
Answer: In general, the major classical Hanafi Fiqh books prohibit the cutting of hair for women. This is also affirmed by many Indian Subcontinent scholars. However, some scholars of the Arab world have permitted it conditionally.
In a Hadith, "the Messenger of Allah (Allah bless him & give him peace) forbade women from shaving their hair." (Sunan Tirmidhi, 2/246 & Sunan Nasa'i, 5/407)
Imam al-Haskafi (Allah have mercy on him) mentions in his famous book in Hanafi Fiqh:
"If a woman cuts her hair, she will be sinful and cursed. In al-Bazzaziyya it is added: "Even with the permission of the husband, as there is no obedience to the creation in disobeying the Creator." (See: Radd al-Muhtar with the Durr of al-Haskafi, kitab al-hazr wal-ibaha, 5/261)
The main two reasons given by scholars for the impermissibility of women cutting their hair are:
a) Imitation of the Kuffar (non-Muslims),
b) Imitation of men,
Both of which have been clearly prohibited in Shariah.
In the Hadith recorded by Imam Abu Dawud in his ‘Sunan' and others, the Messenger of Allah (Allah bless him & give him peace) said: "Whosoever imitates a group is amongst them." (Sunan Abu Dawud, no. 4031)
Regarding the imitation of men, the Messenger of Allah (Allah bless him & give him peace) cursed those men who imitate women and those women who imitate men." (Sahih al-Bukhari, 7/205)
For the above two reasons, the jurists (fuqaha) have generally prohibited the cutting of hair for women. It is for the reason of imitating men; they considered such women to be cursed, as in the Hadith women who imitate men are cursed by the Messenger of Allah (Allah bless him & give him peace)
In view of the above, it would generally not be permitted for women to cut their hair. To imitate the styles of the Kuffar and non-Muslim women is not permissible. The hair cuts prevalent among many modern women have a clear resemblance with the styles of non-Muslim women, thus it will be unlawful.
Similarly, to shorten the hair in a way that it resembles the hair of men is also prohibited. If a woman does so, she will earn the curse of the blessed Messenger of Allah (Allah bless him & give him peace)
However, if a woman trims her hair slightly in a way that she did not contravene any of the above two reasons, then this would be (and Allah knows best) permitted. In other words, there are two conditions for this permissibility, and they both should be understood properly, and not misused or taken out of context:
1) There should be no imitation of non-Muslim Women,
The hairstyles adopted by kuffar and non-Muslim women, such as flicks, perms, fringes, etc... will not be allowed. Cutting the hair from the front will also be impermissible.
2) There should be no imitation of men
Cutting the hair in any way that resembles the hair of men is unlawful (haram), as mentioned previously. Therefore, if a woman cuts her hair from the lower end slightly in order to equate the level of the hairs, then this will be permissible.
It should be noted that, if the hair is cut, then it should be well below the shoulders, and this permissibility is only to cut it slightly. If the woman is married, then this should be done with the consent of her husband.
Finally, it should be remembered that it is better for a woman to not cut her hair altogether, unless there is some genuine reason. In the early times, a woman's beauty was considered in the length of her hair, and not in looking like a man.
In conclusion, generally it is not permissible for a woman to cut her hair. However, if the hair is cut in the manner outlined above, it would be permissible, although better to avoid.
And Allah knows best.

Question: Does the Hanafi School encourage marriage without the guardian's (wali) approval?
Answer: The short and simple answer to your question is that: No, the Hanafi School does not, in any way, promote or encourage a marriage without the approval of one's parents or a legal guardian (wali).
To elaborate: It is a common misconception that the Hanafi School unreservedly allows a marriage without the consent of the woman's parents or her guardian (wali). However, the matter is not as simple as that, and one must understand the Hanafi position properly before coming to any sort of conclusion.
In contrast to the position of most other scholars including the three Sunni Schools of Islamic law, the Hanafi School indeed has some leeway in regards to the necessity of obtaining the consent of the woman's guardian. The relied upon position within the School is that the marriage of a free, sane and adult woman without the approval of her guardian (wali) is valid if the person she is marrying is a "legal" and suitable match (kuf') to her. Conversely, if the person she is marrying is not a legal match to her, then her marriage is considered invalid. (Radd al-Muhtar ala ‘l-Durr al-Mukhtar 3/56-57 & I'la al-Sunan 11/69. For more details and the relevant evidences, please refer to the answer previously posted on this website titled: "Divorced woman marrying without her guardian's approval").
However, this does not mean that such a marriage is encouraged or permitted without any blame. Disobeying one's parents is one of the most serious of sins in Islam, and as such, no School would, and can, allow going against the wishes of one's parents outright. Many Hanafi jurists (fuqaha) have pointed out that it is generally blameworthy and going against the Sunnah to marry without the consent of the Wali regardless of whether the spouse is a legal match or otherwise due to the many Hadiths of the Messenger of Allah (Allah bless him & give him peace) emphasising the importance of having the approval of one's guardian such as: "Any woman who marries without the permission of her guardian, her marriage is invalid, invalid, invalid" (related by Ibn Hibban, Tirmidhi and others, and Tirmidhi considered it a sound/hasan Hadith) and: "There is no marriage without the [permission of a] guardian" (related by Hakim and Abu Dawud). (See: Imdad al-Muftin P: 527)
As such, this Hanafi position is merely a concession (rukhsa) which may be resorted to in situations of need, and a blessing for those sisters who fall victim to their parent's mistreatment and abuse. In cases where parents force their daughters to marry against their wishes based purely on caste, wealth and other similar preferences, and not Islam, and they give importance to their personal gains over and above the interests of their daughters; this position of the Hanafi School can be an important haven. However, the Hanafi School, in no way, gives a green light for sisters to marry themselves without parental approval in all situations, and as such, this position must not be taken as a standard norm upon which marriage contracts are based.
Thus, a woman must first try and convince her parents or Wali to allow her to marry according to her wishes. She may use the intermediary of someone who may be able to influence her parents. Despite trying, if her parents are still being difficult, and her wish is to marry someone based on religious piety, she should present her case to a knowledge, wise and god-fearing scholar who may be able to advise whether she may marry without her guardian's approval or not