Does this require special circumstances or his/her Bishop's permission? Also, if you happen to know, what is the requirements from the Eastern view?
No it does not.
2180 The precept of the Church specifies the law of the Lord more precisely: "On Sundays and other holy days of obligation the faithful are bound to participate in the Mass."117 "The precept of participating in the Mass is satisfied by assistance at a Mass which is celebrated anywhere in a Catholic rite either on the holy day or on the evening of the preceding day."118
118 [link] CIC, can. 1248 # 1.
Can. 1248 §1. A person who assists at a Mass celebrated anywhere in a Catholic rite either on the feast day itself or in the evening of the preceding day satisfies the obligation of participating in the Mass.
§2. If participation in the eucharistic celebration becomes impossible because of the absence of a sacred minister or for another grave cause, it is strongly recommended that the faithful take part in a liturgy of the word if such a liturgy is celebrated in a parish church or other sacred place according to the prescripts of the diocesan bishop or that they devote themselves to prayer for a suitable time alone, as a family, or, as the occasion permits, in groups of families.
Absolutely not. Catholic is Catholic; same faith, different flavor. You may attend Mass in any Catholic Church in communion with Rome.
This is still confusing to many Catholics in the west. Perhaps because we were never 'introduced' to the Eastern Catholic Churches through our religious education programs or homilies. Our pastor, BTW, is bi-ritual; Maronite and Latin Rites. He has both faculties and assists the RC priests in this diocese by saying the NO Mass at a local Catholic hospital. Meanwhile, the RC bishop has closed another 12 churches and those RCs are looking for a new parish. We always welcome visitors and invite them to return. Last Sunday we had an elderly couple who just lost their parish. They loved the Maronite liturgy and its reverence.
Also, if you happen to know, what is the requirements from the Eastern view?
I'm not sure I understand your question. Last year, our pastor had to go home to Lebanon to baptize the newest nephew and take care of some personal business. Not wanting to leave us without a pastor, he sought out a retired RC priest. Initially, the priest was reluctant to say Mass at our parish but Father showed him canonical code to reassure him. While our pastor was away, the RC priest said the NO Mass in our small church and we welcomed him with open arms. He loved the experience!