1) There are some opinions that a person who practices the 8 rakaat tarawih is not considered tarawih, the real tarawih solat actually is 20 rakaat?

Both are accepted, be it 8 rakaat or 20 rakaat, don’t let this be a cause of discord among Muslims, especially tarawih is a sunat practice while avoiding a split is wajib. Some belief the 8 rakaat tarawih is in accordance to what is practised by Prophet Muhammad SAW, but some ulamak said that the Prophet did 8 rakaat at the mosque but complete the 20 rakaat at home so that it does not burden his ummah. They said the 20 rakaat tarawih is practised by Saidina Umar during his reign. (Reference Bidayah Al-Mujtahid)

2) Why are there are four Sects(Mazhab) of faith that is Maliki, Shafi'i, Hanafi and Hambali and there are differences of opinion in the fiqh?

Sect(Mazhab) in hukum was born due to the practice of ijtihad, which started slowly since the time of Prophet Muhammad SAW and continued after his death. It is also cause by the movements of the ‘sahabat R.A.’ to emerging Islamic states. Under normal circumstances the Sect(Mazhab) was formed more widely when the source of guidance is no longer available after the death of the Prophet SAW. The birth of Sect(Mazhab) is founded on two main policies:

1) Possibility of the nas have more than one meaning.

2) Differences in ability and understanding. For the ordinary people who are very limited in the ability to understand the Al-Quran and As-Sunnah as a source of hukum, we adhere to the Shafi'i Sect(Mazhab).

3) While performing major impurity(hadas besar) in the river while diving, do we need to rub the whole body with our hands?

If water reaches the entire body, then the major impurity(hadas besar) is complete. Rubbing your whole body with your hands is sunat while performing major impurity(mandi wajib). (This matter is referred to the book of Matla Al -Badrain in chapter Mandi Wajib p 40)