Hi there! I know I’m a Roman Catholic, but I’ve lurked on these forms enough/been to enough Eastern Catholic churches to give you a somewhat solid answer.
As for the language, there are a variety of language possibilities. From my experience, most Byzantine churches (Ruthenian, Ukrainian, Russian, Melkite, what-have-you) will have a good portion of the liturgy in English. However, the Melkites sometimes have a Arabic Divine Liturgy and the Ukrainians will have a Ukrainian Divine Liturgy.
If this isn’t the case, there are times when certain hymns or chants will be in the mother tongue of that particular Church. For example, the Ruthenians often use Church Slavonic for some music.
As for the Oriental Churches, I’m not really sure.
I’d just say, call the parish and ask. Or, check their website/news bulletin host site and see if the language is listed.
There is no pseudo-conversion that needs to go on. You merely attend the church like you would any Roman Catholic one. Our churches are in communion, that doesn’t mean any conversion is necessary.
Again, just call the parish and let them know you’re coming. They’ll be happy to have you!