If the bleeding lasts for more than 15 days is it still regarded as menstruation, and can she fast?

Praise be to Allah.

There is no definitive evidence in sharee’ah to prove the minimum or maximum length of menses. Shaykh Ibn ‘Uthaymeen was asked: Is there a definitive number of days for the minimum or maximum length of menses? 

He replied: 

There is no definitive number of days for the minimum or maximum length of menses, because Allaah says (interpretation of the meaning): 

“They ask you concerning menstruation. Say: that is an Adha (a harmful thing for a husband to have a sexual intercourse with his wife while she is having her menses), therefore, keep away from women during menses and go not unto them till they are purified (from menses and have taken a bath)”

[al-Baqarah 2:222]

So Allaah did not make the period of abstention a certain number of days, rather He stated that the period of abstention ends when the woman becomes pure. This indicates that the reason for the ruling is menstruation, and whether it is present or not. When menstruation is present, the ruling applies, and when the period ends the attendant rulings no longer apply. Moreover there is no evidence for putting a time limit on menses, even though there was a need (at the time of the Prophet (peace and blessings of Allaah be upon him)) to explain the definition if any such definition had existed. If there was such a definition, it would have been explained in the Book of Allaah or the Sunnah of His Messenger (peace and blessings of Allaah be upon him). Based on this, every time a woman sees the kind of blood which is known to women as being menstrual blood, then it is menstrual blood without that being restricted to a certain time, unless the bleeding is continuous and never stops, or it stops only for a short time such as one or two days in the month, in which case it is istihaadah (non-menstrual vaginal bleeding). 

Majmoo’ Fataawa al-Shaykh Ibn ‘Uthaymeen, 11/271 

Based on this, it is not permissible for you to pray except after the period has ended and you have done ghusl (full ablution). The ending of menstruation may be known from one of two signs: either the emission of a white discharge which comes at the end of the period, or by total cessation of bleeding. 

For more information, see the answer to question no. 5595, where the matter is discussed in more detail. 

And Allaah knows best.