Here is what you are missing from the Code of Canon Law (1983):
Can. 844 §1 Catholic ministers may lawfully administer the sacraments only to catholic members of Christ’s faithful, who equally may lawfully receive them only from catholic ministers, except as provided in §2, 3 and 4 of this canon and in can. 861 §2.
§2 Whenever necessity requires or a genuine spiritual advantage commends it, and provided the danger of error or indifferentism is avoided, Christ’s faithful for whom it is physically or morally impossible to approach a catholic minister, may lawfully receive the sacraments of penance, the Eucharist and anointing of the sick from non-Catholic ministers in whose Churches these sacraments are valid.
§3 Catholic ministers may lawfully administer the sacraments of penance, the Eucharist and anointing of the sick to members of the eastern Churches not in full communion with the catholic Church, if they spontaneously ask for them and are properly disposed. The same applies to members of other Churches which the Apostolic See judges to be in the same position as the aforesaid eastern Churches so far as the sacraments are concerned.
§4 If there is a danger of death or if, in the judgment of the diocesan Bishop or of the Episcopal Conference, there is some other grave and pressing need, catholic ministers may lawfully administer these same sacraments to other Christians not in full communion with the catholic Church, who cannot approach a minister of their own community and who spontaneously ask for them, provided that they demonstrate the catholic faith in respect of these sacraments and are properly disposed.
Can. 861 §2 If the ordinary minister is absent or impeded, a catechist or some other person deputed to this office by the local Ordinary, may lawfully confer baptism; indeed, in a case of necessity, any person who has the requisite intention may do so. Pastors of souls, especially parish priests, are to be diligent in ensuring that Christ’s faithful are taught the correct way to baptize.
From *Redemptionis Sacramentum *(March 2004):
[84.] Furthermore when Holy Mass is celebrated for a large crowd — for example, in large cities — care should be taken lest out of ignorance non-Catholics or even non-Christians come forward for Holy Communion, without taking into account the Church’s Magisterium in matters pertaining to doctrine and discipline. It is the duty of Pastors at an opportune moment to inform those present of the authenticity and the discipline that are strictly to be observed.
[85.] Catholic ministers licitly administer the Sacraments only to the Catholic faithful, who likewise receive them licitly only from Catholic ministers, except for those situations for which provision is made in Can. 844 §§ 2, 3, and 4, and Can. 861 § 2.166 In addition, the conditions comprising Can. 844 § 4, from which no dispensation can be given,167 cannot be separated; thus, it is necessary that all of these conditions be present together.
From *Ecclesia de Eucharistia *(April 17, 2003):
- While it is never legitimate to concelebrate in the absence of full communion, the same is not true with respect to the administration of the Eucharist under special circumstances, to individual persons belonging to Churches or Ecclesial Communities not in full communion with the Catholic Church. In this case, in fact, the intention is to meet a grave spiritual need for the eternal salvation of an individual believer, not to bring about an intercommunion which remains impossible until the visible bonds of ecclesial communion are fully re-established.
What all this seems to say is that non-Catholics (other than members of Eastern churches with valid sacraments) may not receive Communion from a Catholic minister except under very strict conditions, which must ALL be present: there is grave necessity (e.g., danger of death), AND a minister from their own faith is unavailable, AND they have a Catholic belief in the Sacrament, AND they are properly disposed (not in the state of mortal sin).