There were deaconesses, but, as I mentioned in my first post, they were not ordained or given Holy Orders - they were not an exact female equivalent to the male deacon. More information on this is available if you would like. (There are some parties of the Orthodox Church pushing for the re-introduction of Deaconesses, some pushing for actual ordination; much the same as don’t denounce homosexuality, divorce, birth control, all abortion, and a married episcopate: this is obvious from the notes in the Orthodox Study Bible - produced by Protestant converts to Antiochene Orthodoxy - on First Timothy.)
Any person, priest or not, Christian or not, can baptize another, granted that he has the intent to baptize. And, it seems your history is a bit shaky - infant baptism always was the norm, from the Apostolic age and the first second generation Christians, although in some ages and in some classes of people (nobility), there are legends (apocryphal or not) that men were not baptized until their marriage, so that their fornications and other pre-matrimonial sins would be erased. Examples like Constantine, baptized on his deathbed, are rare, and never the norm.
Hoffen: that women are ontologically incapable of ordination implies ontological inferiority, and is the most hard-line or traditionalist philosophical position advanced against the ordination of women. It is also the most secure and logical, being as it is based in first principles. However, there are an entire array of arguments on both sides, many of which, on the no-priestesses side, have nothing to do with ontology. However, they tend to be less secure, because they’re either culturally conditioned (CBMW, egalitarians), based solely in Scripture (complementarians, Patriarchalists), or are “scientific”, being supposedly empirical, physicalist, and fact-based instead of grounded in God, first principles, and logic, and, as everyone has a different opinion but must share the same facts, the same facts are merely interpreted differently by each side, lacking decisiveness.