Yes, "Latin Rite" is generally used synonymously with "Roman Rite" and vice versa.

Not really sure what you are asking here, the "Roman" Church might be a way of referring to the Latin Rite of the Catholic Church, or it might be referring to the diocese of Rome. Assuming you are referring to the Latin Rite, then the Byzantine Church also is a Rite within the Catholic Church, it is not as large as the Latin Rite, but it is every bit as ancient, and just as much a part of the Catholic Church as the Latin Rite. Are using asking for the physical differences between an actual Church of the Latin Rite as opposed to a Church of the Byzantine Rite?

Eastern rite and Latin rite Catholics both belong to the same Church under the leadership of the pope and share the same Gospel values.

In England, and the rest of the Latin Rite Church, the Eucharist was in Latin, in the Greek Rite, it was in Greek, Maronite Rite is was in Syriac (Christian Aramaic).

properly/fairly