When was the Filioque clause added to the creed and what is the reason for that? Did the eastern fathers believe in the filioque?
First, to clarify: The Filioque refers to the Latin phrase "and the son," to describe the internal "economy" of the Trinity. It describes the Holy Spirit as proceeding from the Father and the Son, as opposed to from the Father only. The Council of Nicaea  required only that a believer stipulate "I believe in the Holy Spirit." The Council of Constantinople  described the Holy Spirit as "proceeding from the Father."
The answer to the question "When was the Filioque clause added to the creed?" depends on whether one is speaking of individual church fathers, local churches, papal usage, Catholic liturgy, or ecumenical councils. Several Western Fathers used the clause prior to 381. The Council of Seleucia-Ctesiphon in Persia [c. 410] reportedly used it as well. However, most Eastern churches and teachers abided by the ruling of 381, insisting that only another ecumenical council could change it.
In the 9th century, Pope Leo III used the Filioque, stating that "the Holy Spirit is Complete God begotten of the Father and the Son." It was also endorsed by the Council of Aachen in 809 convened by Charlemagne and governing the practice of the churches under his sovereignty. However, this usage offended Eastern churchmen, who considered the Filioque to violate the teaching of the ecumenical council of 381. The issue became a major international controversy when Patriarch Photius of Constantinopol accused the western church of heresy for using it and attempted to effectively ban its use. In 867 one of several councils held under Photius' leadership excommunicated Pope Nicholas I for using the Filoque and declared the teaching anathema.
The Filioque became a formal part of the Latin rite in Rome in 1014 under Pope Benedict VIII. The issue became the crucial theological question of the East-West Schism
The Filioque clause was generally rejected by the Eastern fathers, especially after 381. The year 1014 is a good a date as any to understand when it became part of Catholic tradition, although Leo III's endorsement in the early 9th century is also a candidate.