All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The used water is of two kinds.
First, the remaining water in the receptacle after ablution or Ghusl (ritual bath) of a male is pure and can be used for purification and removing impurity without any difference of opinion among the scholars as far as we know.
The remaining water after ablution or Ghusl of a female is pure as well and can be used for purification and removing impurity, according to the view of the majority of the scholars.
The evidence for this is the Hadeeth of Ibn ‘Abbaas who said: “One of the Prophet's wives performed Ghusl from a receptacle, then the Prophet, sallallaahu ‘alayhi wa sallam, came to perform Ghusl from the remaining water in that receptacle. His wife said: “I was in the state of sexual defilement. He said: “The water does not become impure.” [Ahmad, Abu Daawood and An-Nasaa’i]
Ibn ‘Abbaas said that the Prophet, sallallaahu ‘alayhi wa sallam, used to perform Ghusl from the water that remains after having been used by his wife Maymoonah to remove her state of sexual defilement.
Second, the water that drips from the organs of the person after he performs Ghusl or ablution: this is also used water and it is of three types:
1. The water which is used for cleaning or refreshing and cooling off oneself is pure without any disagreement as far as we know. Ibn Qudaamah said: “The water used for cleaning and cooling off or refreshing oneself is pure and there is no difference of opinion in this matter.”
2. The water which is used to acquire an obligatory ritual purity: the scholars have different opinions concerning this water. Some are of the opinion that it is pure but can not be used for purification; the others are of the opinion that it is absolutely pure and can be used for purification and for the removal of impurity. This is the predominant opinion which is adopted by ‘Ali, Ibn ‘Umar, Abu Umaamah Al-Hasan, ‘Ataa’, An-Nakha’i, Az-Zuhri and Imaam Ahmad . This is also the opinion of the Maaliki School and one of the opinions of Ash-Shaafi’i School.
3. The water which is used to get a desirable ritual purity such as to renew an ablution or to have a Friday Ghusl (according to those who say that it is desirable), the preponderant opinion is that such water is also absolutely pure. This is one of the opinions of Imaam Ahmad and it is also the opinion of the Maaliki School and others.
Therefore, the water which drips from a person into a receptacle that contains pure water does not affect the water regardless of its quantity.
As for your question about opening an institute to teach life-insurance, then this is forbidden since the procedure of contemporary life-insurance which depends on taking people's money without due right is prohibited. For more benefit in this regard, please refer to Fataawa 81441 and 84978.
Therefore, teaching such subjects is a true cooperation in spreading what is forbidden and training people how to use it. One cannot be free from sin by merely informing students of its prohibition while teaching them.
As regards bank transactions and dealings in Islamic banks, then please refer to Fatwa 83941.
The basic difference between an Islamic bank and a non-Islamic bank is that the basis of a non-Islamic bank is taking extra amount from the debtors against giving them loans, and this is pure Riba (interest and or usury), while Islamic banks invest the money in lawful activities such as partnership, Muraabahah (please refer to Fatwa 83725 in this regard) and other lawful transactions. So, Islamic banks and non-Islamic banks can not be made equal.
Allaah Says (what means): {Then is one who was a believer like one who was defiantly disobedient? They are not equal.}[Quran 32: 18-19]
Allaah also Says (what means): {Then will We treat the Muslims like the criminals? What is [the matter] with you? How do you judge?}[Quran 68:35-36]
Allaah Knows best.