Monica,
You often point out to others their imprecise use of language.  The Latin Church does not "accept" the rites that you list.  Those rites are practiced within the Latin Church.  There is no "Eastern Church" as such.  There is a number of Eastern rites (and you forgot the Byzantine rite, which is the largest).  These rites are practiced by the various Eastern Catholic Churches.  All of those Churches, along with the Latin Church, form the universal Catholic Church.  The various Churches which form the Catholic Church celebrate the Liturgy in accordance with the rite that the particular Church uses.  The conversation about translations from Latin applies only to the Churches of the Latin rite.  The non-Latin rite Churches never used Latin for their liturgical celebrations.  Some have translated the Liturgy into their modern languages; others have not.