When Christianity was first introduced were women allowed to become a priest or bishop?

Answer 1

No.

We read in the writings of the Church in the Apostolic Age:

Let your women keep silence in the churches...and if they will learn any thing, let them ask their husbands at home (1 Cor 14:34-35)

I do not allow a woman to teach or exercise authority over a man (1 Tim 2:12)

Even by 500 AD (still in the time of the Early Church) the Bishop of Rome wrote:

Yet we have heard with irritation that divine things have come to such lack of respect that women are encouraged to minister at the sacred altars and to perform all the things that do not belong to them, which are assigned only to the service of men.

A figure of "helper", termed "deaconess", was found early in the Church - but she was not ordained, meaning she was not like an ordained deacon, and much less like a priest or bishop (successor of the apostles). This is evident by the same writings that prove the existence of these roles.

Church Father Epiphanius of Salamis (310-403 AD) wrote:

It is true that in the Church there is an order of deaconesses, but not for being a priestess. From this bishop [James the Just] and the just-named apostles, the succession of bishops and presbyters [priests] in the house of God have been established. Never was a woman called to these. If women were to be charged by God with entering the priesthood or with assuming ecclesiastical office, then in the New Covenant it would have devolved upon no one more than Mary to fulfill a priestly function. She was invested with so great an honor as to be allowed to provide a dwelling in her womb for the heavenly God and King of all things, the Son of God... But He did not find [the conferring of priesthood on her] good.

The Apostolic Constitutions (400 AD) specifies:

Chose as a deaconess a faithful and holy woman for the ministry of women... For we need a female deaconess for many things.. A deaconess does not bless or do any of the things priests and deacons do, she just takes care of the doors and ministers when women are baptized, for the sake of propriety.

Several Councils speak of this.

Council of Nicaea I (325 AD), Canon 19:

Similarly, in regard to the deaconesses, as with all who are enrolled in the register, the same procedure is to be observed. We have made mention of the deaconesses, who have been enrolled in this position, although, not having been in any way ordained, they are certainly to be numbered among the laity.

Council of Laodicea (372 AD):

So-called presbyteresses or presidentesses should not be ordained...It is not right for women to have access to the altar.

Council of Nimes (394 AD), Canon 2:

There is a report that women seem to have been, we know not in what place, admitted to the levitical ministry, contrary to apostolic discipline,and unknown until today....an ordination of this sort must be annulled, and care taken that no one for the future be so bold.

Council of Orange I (441 AD), Canon 15:

Deaconesses are certainly not to be ordained,and if there are some,they must bow their head under the blessing given to the people.

Sixth Council of Paris (829 AD), Canon 49:

That women must not go to the altar is abundantly found in the Council of Laodicea, and in the decrees of Pope Gelasius. So this so illicit a thing, entirely abhorrent to the Christian religion, is forbidden for the future.

The definitive and unchangeable modern statement of the Church is found in Ordinatio Sacerdotalis (1994):

Priestly ordination, which hands on the office entrusted by Christ to his Apostles of teaching, sanctifying and governing the faithful, has in the Catholic Church from the beginning always been reserved to men alone.

Wherefore, in order that all doubt may be removed regarding a matter of great importance, a matter which pertains to the Church's divine constitution itself, in virtue of my ministry of confirming the brethren I declare that the Church has no authority whatsoever to confer priestly ordination on women and that this judgment is to be definitively held by all the Church's faithful.