...that was the catalyst for further thought on why the rituals are there. No-one has addressed whether they directly come from Jesus himself or whether some church father has added them as time has gone on.
To discuss in detail the development of the rites of Christian initiation would be difficult to do in a forum post, but I'll try to sum it up.
Baptism, as a ritual washing away of sins and a dedication to a new way of life, begins, as we know it as Christians, with the ministry of John the Baptist. Jesus himself is baptised by John, does some baptising himself, and commands that believers be baptised in the name of the Father, and of the Son, and of the Holy Spirit. Beyond that, he doesn't say much.
The technique of the washing is adapted from Jesus' own baptism, which reflects earlier practices. If at all possible, we immerse fully three times, but forms of washing, pouring water over the head, etc., have been accepted as (at least sometimes) valid, even becoming normative in some traditions. In conjunction with the baptism, there was a laying on of hands and prayer for the reception of the Holy Spirit, which is now done in the form of post-baptismal anointing with chrism, a specially consecrated oil. These, in turn, prepare the person to receive the Eucharist, and it is the Eucharist which completes and fulfills this process.
There was a traditional period of preparation before baptism which involved hearing/reading the Scriptures, learning the faith of the Church, the basics of a life of prayer, etc., which we know as "catechumenate". It had a varying length in different places. The passage of certain stages would be marked by certain rites: prayers would be said over the person to exorcise them, to pray for their purification and that they might learn the faith properly and live accordingly, they would be asked to reject Satan and confess their faith in Christ, they would be taught the Creed of the Church in order to confess it publicly, etc.
What you experience nowadays as the service of baptism in a church is really all of these "individual moments" in the initiation process (which in the early Church would've been done over a period of weeks or months) done in succession, one after the other, in the space of an hour or so. If you separated them and did them in the proper order at the proper intervals, it might take a few minutes for each "moment", but you'd have to do it over the course of several months. Our custom for well over a thousand years now has been to do them all in one shot.
The basic order of the service is the same in all the extant liturgical traditions, but since these developed in different parts of the world, there are some customs that are not universal. For instance:
Really, I also gave a specific instance about the baby being held up and moved in the sign of the cross.
Seriously, someone here must be Greek and can answer that one action?
I'll defer to Greeks, but I think what you're describing may have to do with a separate "moment" which has been attached to the rite of baptism: this "moment" is called "churching". This developed as a way to progressively introduce newborn children into the community of the Church and to reintegrate recently delivered mothers back into the community after their absence and recovery. Prayers are said for the child and the mother at certain milestones: immediately after birth, eight days after birth, and the churching itself, which is supposed to occur forty days after birth (there is some variation on this). Some traditions include a rite in which the priest takes the child and presents him/her before the altar, carries him/her in, etc. It's a blessing, a form of dedication, an imitation of Christ's own entrance into the Temple in Jerusalem at forty days old. Traditionally baptism would be some time after this, but as people began to baptise babies before the forty days were up, it became customary to add these rites to the baptismal rite in some way.