Okay very broad question, but What do the different rites encompass? Do they worship differently, do they worship together or do they have separate Rite Chapels? why do some Rites no longer exist (eg. Celtic)?
How different are the Eastern Orthodox from The Eastern(Byzantine?) Rite?
Do Catholics accept other denomination baptisms?
Yes, the way of worship can vary somewhat but all adhere to the basic doctrines of the Latin Rite. We have separate places where we worship, but one could easily go to another and say accept Holy Communion with no difficulty.
From what I know about the Eastern and Byzantine, they both have the altar behind closed gates that separate it from the congregation. But other than that the Byzantine look to the Bishop of Rome as the head Bishop, the EO does not.
We most assuredly recognize the baptisms of these other Catholic affiliated churches, in fact the Catholic Church even recognizes the baptisms of Protestant sects, provided the baptism is done in the proper manner, i.e. in the name of the Father, the Son, and the Holy Ghost.