Also, can the members of the Orthodox church receive communion in the Roman Catholic Church?
Tony, this is treated in canon 844 “§3. Catholic ministers administer the sacraments of penance, Eucharist and anointing of the sick licitly to members of Eastern Churches which do not have full communion with the Catholic Church if they seek such on their own accord and are properly disposed. This is also valid for members of other Churches which in the judgment of the Apostolic See are in the same condition in regard to the sacraments as these Eastern Churches.” * Both conditions --seeking of their own accord and proper disposition-- would need to be met.
The Orthodox are Eastern Churches that do not have full communion with the Catholic Church. Such “other Churches” as judged by the Apostolic See include among them the Polish National Catholic Church and the Church of Assyria. There are others.
Baptized non Catholics, such as an Anglican, might conceivably receive under very restrictive conditions. All the conditions would have to be met. In particular, the person would have to have Catholic faith in these sacraments, believe in the real presence, and this would not be the formal doctrine of their churches in most cases. (Then too, as noted, there is the question of the invalidity of their priestly orders and hence of their communion as Della posts about Anglicans. Yet even though their eucharists be invalid, an individual Anglican might still have the Catholic faith in the Eucharist.) The conditions are expressed in paragraph four of the same canon.
Canon 844 “§4. If the danger of death is present or if in the judgment of the diocesan bishop or the conference of bishops, some other grave necessity urges it, Catholic ministers administer these same sacraments licitly also to other Christians not having full communion with the Catholic Church, who cannot approach a minister of their own community and who seek such of their own accord, provided that they manifest Catholic faith in these sacraments and are properly disposed.” Urgent need might include imprisonment, persecution.
But note canon 844 §5 “For the cases mentioned in §§ 2, 3, and 4, the diocesan bishop or conference of bishops is not to enact general norms except after consultation at least with the local competent authority of the interested non-Catholic Church or community.”
The state of grace is presumed with the term proper disposition, and of course baptism is necessary (some “Christian” churches don’t baptize or baptize inefficaciously).
As to the other way around, canon 844: "§2. Whenever necessity requires or true spiritual advantage suggests it, and provided that danger of error or of indifferentism is avoided, the Christian faithful for whom it is physically or morally impossible to approach a Catholic minister are permitted to receive the sacraments of penance, Eucharist, and anointing of the sick from non-Catholic ministers in whose Churches these sacraments are valid. " This would include, by way of partial example, the Orthodox, the Polish National Catholic Church. It would not include the Anglicans and other non Catholic Christians in general. But all conditions would have to be met (avoid danger of error or indifferentism, impossibility of access to a Catholic minister).
(* 1983 translation)