There are various rites in the Catholic Church. This means primarily that there are various ways to celebrate the liturgy, though the different rites have their own set of laws and disciplines in other areas as well, such as the rules for fasting and abstinence during lent. A priest of the eastern rite is a Catholic priest who is a member of the eastern rather than the latin rite (the rite the majority of Catholics belong to).
yes
LAMA
priest
No. There has been some confusion over the years because the term for the wife of a priest is the feminine form of the word "priest" (presbytera). But she is in no way a priest.
No - he is Eastern Orthodox Christian. His father is a priest.
An archpriest is a rank given to a married priest in the Eastern Orthodox Church, or an honorific title bestowed upon a priest with a specific function in the Roman Catholic church.
In the Roman Catholic Church, it is required that a priest be celibate. This is to keep the priest from being distracted from doing God's will as a priest. However, if an Anglican or Orthodox priest who is married converts to Catholicism he is able to become a Catholic priest and keep his wife. In the Eastern Catholic Church though, the priests are allowed to marry though. Lutheran and Episcopalian Priests are allowed to marry as well.
Depending on the situation he may be addressed as Father (in person) or Reverend Father (in writing). In Eastern Christianity we use the priest first name (ex. Father James)
A female has never been ordained to "major orders" deacon/priest in the Roman Catholic Church, the Uniate Churches (Eastern Catholic) or Orthodox Church
These are led by the priest in Church. Lay people do not lead prayers in Church. In some instances, such as during Vigil services, the priest will start the prayers, and then lay people continue to read them. But where a priest is present with lay people, only he can lead the prayers.
Wikipedia"Archpriest is the title of a priest who has supervisory duties over a number of parishes. The term is most often used in Eastern Orthodoxy and Eastern Catholic Churches, although it may be used in the Latin rite of the Roman Catholic Church instead of dean or vicar forane."For further reads, see link below.
In a formal way you can write down "Rev.", but less formal is "Fr.". If you address a priest while you are speaking with him, he is called "Fr. ...". For example: "Father Robert". This is how it is done in the USA. I am not sure if you address a priest differently outside the USA.