*** Let him bring in the priests of the church and let them pray over him...***
***The offices of "bishop, priest (presbyter) and deacon..." ***
Both of you are translation Presbuteros (elder) as priest. Why is that?
Is not the Greek word for priest "Hiereus"?
Not necessarily. "Hiereus" is a generic word for "religious leader," coming from the root word "hier," meaning "holy."
Etymologically, the English word "priest" (which, of course, originally described Catholic clergy) comes from "presbyter". "Bishop" comes from /episcopos/, "overseer". The overseers and elders described in the NT are bishops and priests, respectively.
There is no blanket permission for all Christians to go around administering this Sacrament. James is clear that the "presbyteros ecclesiae" should be called, not just anyone.
As for whether a presbuteros is a priest, I don't know of any other kind of man who can forgive sins: "and if he be in sins, they shall be forgiven him". Likewise, since the Eucharist is a propitiatory sacrifice for sin (cf. Lk 22:19-20; 1 Cor. 10:16-21), it follows that the ministers of the Eucharist are true priests (cf. Heb. 5:1). Ancient and apostolic tradition restricts the celebration of the Eucharist to presbyters and bishops, therefore it follows that they are true priests.
And now as to prescribing who ought to receive, and who to administer this sacrament, this also was not obscurely delivered in the words above cited. For it is there also shown, that the proper ministers of this sacrament are the Presbyters of the Church; by which name are to be understood, in that place, not the elders by age, or the foremost in dignity amongst the people, but, either bishops, or priests by bishops rightly ordained by the imposition of the hands of the priesthood. ... If any one saith, that the Presbyters of the Church, whom blessed James exhorts to be brought to anoint the sick, are not the priests who have been ordained by a bishop, but the elders in each community, and that for this cause a priest alone is not the proper minister of Extreme Unction; let him be anathema. (Council of Trent, Session XIV, Decree and Canons On Extreme Unction)