In Roman Catholicism, how far back in history does the process (Sacrament) of Confirmation go? Does the Sacrament of Confirmation go back to the early Church?  Also, has it always occurred around the age 14 (except in situations where it would occur later, such as conversions)?
According to the Catholic Encyclopedia, the sacrament of Confirmation comes directly from the beginning of the Church, as performed by the Apostles, and thus, it is part of the Oral Revelation (or Tradition, Living Magisterium), and partly seen in the Written Revelation (i.e. the Scriptures). The Encyclopedia states:

The Sacrament of Confirmation is a striking instance of the development of doctrine and ritual in the Church. We can, indeed, detect much more than the mere germs of it in Holy Scripture; but we must not expect to find there an exact description of the ceremony as at present performed, or a complete solution of the various theological questions which have since arisen. It is only from the Fathers and the Schoolmen that we can gather information on these heads.

Then there are two quotes used to support this Biblical basis:

We read in the Acts of the Apostles (8:14-17) that after the Samaritan converts had been baptized by Philip the deacon, the Apostles &quot;sent unto them Peter and John, who, when they were come, prayed for them, that they might receive the Holy Ghost; for he was not yet come upon any of them, but they were only baptized in the name of the Lord Jesus; then they laid their hands upon them, and they received the Holy Ghost&quot;.
Again (19:1-6): St. Paul &quot;came to Ephesus, and found certain disciples; and he said to them: Have you received the Holy Ghost since ye believed? But they said to him: We have not so much as heard whether there be a Holy Ghost. And he said: In what then were you baptized? Who said: In John's baptism. Then Paul said: John baptized the people with the baptism of penance . . . Having heard these things, they were baptized in the name of the Lord Jesus. And when Paul had imposed his hands on them, the Holy Ghost came upon them, and they spoke with tongues and prophesied&quot;.

From them, the author concludes:

From these two passages we learn that in the earliest ages of the Church there was a rite, distinct from baptism, in which the Holy Ghost was conferred by the imposition of hands (dia tes epitheseos ton cheiron ton Apostolon), and that the power to perform this ceremony was not implied in the power to baptize.

The article goes on to expose evidence and support for the rite later in history, including the Church Fathers.
This perspective is part of the Catholic doctrine, as expressed in the Cathecism (and quoting Paul VI's apostolic constitution Divinae consortium naturae):

1288 &quot;From that time on the apostles, in fulfillment of Christ's will, imparted to the newly baptized by the laying on of hands the gift of the Spirit that completes the grace of Baptism. For this reason in the Letter to the Hebrews the doctrine concerning Baptism and the laying on of hands is listed among the first elements of Christian instruction. the imposition of hands is rightly recognized by the Catholic tradition as the origin of the sacrament of Confirmation, which in a certain way perpetuates the grace of Pentecost in the Church.&quot;


Finally, regarding the age of baptism, as stated in the comments by Ken Graham, the Eastern Rites (and the Orthodox Church, in which the sacrament is called Chrismation) performs both sacraments together, whereas the Latin Rite and Western church performs them separately. The same page of the Catechism linked above states:

1290 In the first centuries Confirmation generally comprised one single celebration with Baptism, forming with it a &quot;double sacrament,&quot; according to the expression of St. Cyprian. Among other reasons, the multiplication of infant baptisms all through the year, the increase of rural parishes, and the growth of dioceses often prevented the bishop from being present at all baptismal celebrations. In the West the desire to reserve the completion of Baptism to the bishop caused the temporal separation of the two sacraments.

Regarding particularly the Western church, the age at which the confirmation was administered varied considerably. For example, the Encyclopedia states:

It was especially during the thirteenth century that vigorous measures were taken to secure the proper administration of the sacrament. In general, the councils and synods direct the priests to admonish the people regarding the confirmation of their children. The age limit, however, varies considerably. Thus the Synod of Worcester (1240) decreed that parents who neglected to have their child confirmed within a year after birth should be forbidden to enter the church. The Synod of Exeter (1287) enacted that children should be confirmed within three years from birth, otherwise the parents were to fast on bread and water until they complied with the law. At the Synod of Durham (1217? Cf. Wilkins, loc. cit. below) the time was extended to the seventh year.

The latter became, later on, the custom. The Encyclopedia states:

Further, when infant baptism became customary, confirmation was not administered until the child had attained the use of reason. This is the present practice, though there is considerable latitude as to the precise age. The Catechism of the Council of Trent [(1545-1563)] says that the sacrament can be administered to all persons after baptism, but that this is not expedient before the use of reason; and adds that it is most fitting that the sacrament be deferred until the child is seven years old, &quot;for Confirmation has not been instituted as necessary for salvation, but that by virtue thereof we might be found well armed and prepared when called upon to fight for the faith of Christ, and for this kind of conflict no one will consider children, who are still without the use of reason, to be qualified.&quot;

This custom of the use of reason being reached at age 7 continues to be in the Canon Law today, under the title &quot;age of discretion&quot;, as can be seen here.
This shows that Confirmation was indeed administered at quite different ages across the centuries, and far from the custom of 14 years old, as in some countries today.