Rites of Christian Initiation for Adults (RCIA) generally refers to the process through which Non-Catholic adults (generally over the age of 7) are received into the Church. They receive of course sacraments of initiation, baptism (if not already validly baptized), confirmation and Eucharist (first communion) as the climax of this process, which also includes preparatory rites that punctuate the period of preparation.
The age at which baptized Catholics receive first communion and confirmation is up to the bishop’s conference of the country (which also has adapted the RCIA for their country). In the Latin Rite these are any time after the age of reason (generally age 7). The actual age, and the sequence of celebrating the sacraments, is up to the local ordinary (bishop). In the USA it first communion is generally celebrated in 2nd or 3rd grade, and confirmation may be conferred on Catholic children anytime between 7 to 18.
There is a movement, prompted in part by the restoration of the RCIA and various catechetical documents which call for “restoration of the order of initation” to move confirmation before first communion, or to celebrate them together, in various dioceses. Some parishes within some dioceses have been given permission to experiment with this. Even in our own state of Texas, each diocese is different and ages are all through that range. Here (Brownsville) first communion is in 3rd grade, Confirmation in 10th. But I have children transferring from other dioceses who have already been confirmed in 4th or 4th grade. It is all over the map.
According to RCIA the priest who baptizes at the Easter vigil has the faculty to confirm and in fact must confirm those whom he baptizes. Whether or not he can confirm baptized non-Catholics, or Catholics, depends on the bishop and what he delegates or whether he prefers to reserve Confirmation to himself. He may appoint priests to assist him in confirming, in special instances or as a general practice. The priest who is given that faculty must use it for those for whom it has been granted.
As far as preparation for Confirmation, that again depends on the requirements of each bishop. In general the child (or adult) must be catechized on the meaning of the Creed, because he makes a profession of faith, and on elements of the Christian Life. Homeschoolers should consult their pastor or the catechetical office of their diocese for requirements on sacramental preparation.
This entire discussion is about the Latin Rite so there is no need to bring up on this thread practice of the Eastern Rites which is generally to confirm and baptize infants at the same time and to administer communion at that time. There is good theology that supports this. Equally there is a history of theology that supports the delay of communion and confirmation to the age of reason, as now practice in the West.