Anyone of any age is welcome to receive Holy Baptism. All people, regardless of age, mental acuity, and intellectual ability, are welcome to Christ.
I believe it is the growing custom within the Anglican Church that, when a person is baptized, chrism is also imputed. I've seen baptisms at all three of the Episcopal parishes I've been involved with: one on the broad/lower side and the other two on the broad/higher side, and each included chrism.
Whether this is considered a sacrament is up to debate. Again, increasingly, you are going to find that Anglicanism is going into the direction of "reunifying" both "halves" of Christian Initiation. As you are probably aware, in the West, Baptism and Confirmation are truly two halves to what you EOs (OOs too, I believe) practice. In Anglicanism, this too was the case, but in recent decades, the divines in the Anglican Church are arguing for the restoration of the full initiatory rite in one service As such, many bishops in their respective dioceses are either asking or at least allowing their clergy to include a chrismation along with all baptisms.
It should however be pointed out that, for adult or teenage converts, it has often long been the practice that catechism precede Baptism, which was usually done upon a traditional day, like the Great Paschal Vigil, All Saint's Day, or when the bishop makes his or her early visitation. In those cases, with the bishop present, the individual receives Baptism, Confirmation, and their first Communion at the same time. The issue above is really more to do with infants and younger children along with teens and adults who are to be baptized but the bishop won't be there.
The question I suppose truly boils down to whether a priest has the Apostolic authority to administer the entirety of Christian Initiation or not. Again, the growing Anglican opinion seems to be in the direction of "yes with a bishop's approval and under the understanding that it is under the bishop's authority and blessing." After all, priests cannot consecrate oils; that is the bishop's responsibility. And for all of those baptisms, since they were never with a bishop present, each time the priest said that the bishop was the one responsible for the oil's consecration.
So currently, the answer is both no and yes, but increasingly more yes than no.
As for Communion, since Baptism is the gateway to all other sacraments, there is no reason why even an infant couldn't receive Communion. I do not believe this to be, at the moment, a very common practice, but there isn't actually anything officially Anglican that says that it cannot. When I have seen especially young children receive, the parent or guardian usually asks the chalice-bearer not to give their young one that element. Some chalice-bearers simply without it, but usually out of an ignorant assumption of a parent's wishes. Again, I must emphasize that it isn't the Church barring the young one from receiving from the chalice, but the parent or other legal guardian. Furthermore, we always must remember that, in each element is not just the Body or the Blood but both always together. So even in those instances, the entirety of Jesus' Being is being received and consumed.
There is truly no concept of "First Communion" like which currently exists in the Vatican Catholic Church. At my current parish, one of our new acolytes is a great young boy who has received Baptism yet has not Confirmed (I have no clue whether he received chrism at his baptism). Yet when the acolytes receive, he accepts both elements (and I assure you all that, with me as his teacher, he will be educated to understand the great and awesome significance which is Holy Communion!).
However, in one of my old parishes, the assistant priest (she now is the rector of her own parish; lucky people!) taught a class to many of the youngers about that particular sacrament. For graduation, there was a special ceremony and it was considered to be the first time they received Holy Communion with the new knowledge, understanding, and most of all appreciation that they now possessed. So there is that sense of a "First Communion," but in reality, if you've been Baptized, no matter how old or young, you are welcome to receive.
