In theory. In practice, the monastery selects a hieromonk of the schema to do so when the bishop asks for one, or when the extant one is overly full.
Ruthenian and Ukrainian are both slavic Tradition (sub-rite) there is no slavic rite. Both are further of the Ruthenian Recension, while the Russians are Nikonian Recension.
Byzantine Rite, and either Ruthenian or Ukrainian Church, depending upon which house.
It’s vaguely possible, but not advisable. You must be formed in the rite of the church to which you will incardinate. Preferably in their own seminary, when possible. The requirements for the Byzantine ones are a bachelor’s degree… in just about anything… and the bishop’s permission.
They aren’t. Their remnant/dissent portion of the synod when they came into union is now known as the Antiochian Orthodox.
The ones up here (Alaska) generally are ascribed to the Russian Church Sui Iuris, and promptly request change of enrollment to the Roman.
Yes. It’s part of the Muscovite Patriarchate of the Russian Orthodox, and functions in a manner similar to a Sui Iuris church - autonomous under their own hierarchs, but answerable to the patriarchate. Therefore, as part of a canonical body, there is no question that they have valid sacraments.