Does the priest know he is giving Holy Eucharist to Non-catholics?   Only Baptized Catholics may receive.

From the Code of Canon Law;

Can.  844 §1. Catholic ministers administer the sacraments licitly to Catholic members of the Christian faithful alone, who likewise receive them licitly from Catholic ministers alone, without prejudice to the prescripts of §§2, 3, and 4 of this canon, and ⇒ can. 861, §2.
§2. Whenever necessity requires it 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.
§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.
§4. If the danger of death is present or if, in the judgment of the diocesan bishop or 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 on their own accord, provided that they manifest Catholic faith in respect to these sacraments and are properly disposed.
§5. For the cases mentioned in §§2, 3, and 4, the diocesan bishop or conference of bishops is not to issue general norms except after consultation at least with the local competent authority of the interested non-Catholic Church or community.


http://www.vatican.va/archive/ENG1104/__P2T.HTM

From the Code of Canon Law;

Can.  844 §1. Catholic ministers administer the sacraments licitly to Catholic members of the Christian faithful alone, who likewise receive them licitly from Catholic ministers alone, without prejudice to the prescripts of §§2, 3, and 4 of this canon, and ⇒ can. 861, §2.
§2. Whenever necessity requires it 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.
§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.
§4. If the danger of death is present or if, in the judgment of the diocesan bishop or 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 on their own accord, provided that they manifest Catholic faith in respect to these sacraments and are properly disposed.
§5. For the cases mentioned in §§2, 3, and 4, the diocesan bishop or conference of bishops is not to issue general norms except after consultation at least with the local competent authority of the interested non-Catholic Church or community.


http://www.vatican.va/archive/ENG1104/__P2T.HTM

I am not questioning the validity and binding force of the 1983 CIC --- I accept it --- but I think the OP was wondering more about practices prior to Vatican II, under the 1917 CIC and even before.

This did happen, many times some orthodox churches were in communion with both Rome and Constantinople. Mostly it did occur between oriental orthodox and oriental catholics. The reason is that there's never been an official condemnation of these churches. At Chalcedon for example only the patriarch of Alexandria was condemned but not for heresy for issuing an illegitimate excommunication. Technically the Antiochians Syriacs just issued anathemas and withdrew. Armenians had no part in the council. They simply were outside the Empire. The churches just separated essentially because each linguistic group was using philosophical terms that were different from each other and the political ambition of Constantinople was unchecked, this essentialy was the thing that lead them to break with Rome. Rome began in earnest to send missionaries to these churches and over @ 200 years restored communion to many. The discussions lead to the healing of many misconceptions and at times the allowing of communion. This is different than the EO who are essentially just heretics. Having explained all that, it was never a blanket permission, or common practice.

This did happen, many times some orthodox churches were in communion with both Rome and Constantinople. Mostly it did occur between oriental orthodox and oriental catholics. The reason is that there's never been an official condemnation of these churches. At Chalcedon for example only the patriarch of Alexandria was condemned but not for heresy for issuing an illegitimate excommunication. Technically the Antiochians Syriacs just issued anathemas and withdrew. Armenians had no part in the council. They simply were outside the Empire. The churches just separated essentially because each linguistic group was using philosophical terms that were different from each other and the political ambition of Constantinople was unchecked, this essentialy was the thing that lead them to break with Rome. Rome began in earnest to send missionaries to these churches and over @ 200 years restored communion to many. The discussions lead to the healing of many misconceptions and at times the allowing of communion. This is different than the EO who are essentially just heretics. Having explained all that, it was never a blanket permission, or common practice.

No, this has never been permitted in principle.  What you're discussing is merely a dispute or uncertainty of fact about whether they were Catholic.  Had it been clearly established that they were not Catholic, then they would be forbidden from receiving the Sacraments.  It is of unanimous Apostolic Tradition that those outside the Church may not receive the Sacraments.  So, uhm, no, this "did [NOT] happen" ... contrary to your claim.