1 Cor 14:34 Women should keep silent in the churches, for they are not allowed to speak, but should be subordinate, as even the law says.
The question of to which law does Paul refer has come up. Is it the Mosaic law or the Roman law or some other law?
I looked for a cross reference in the Mosaic law where it says "women are not allowed to speak", but didn't find anything.
Besides, there are a number of females that Paul congratulates for "speaking up". Timothy's mother and grandmother, Phoebe, Justia, Lydia, the women (and men) of Acts 9:2, and others. And of course, there's the gender neuter of the all in Christ.
As to Roman Law, this was said,
Women had limited engagement with politics in the public sphere; among the elite, moralists extolled female domesticity. Rome's political system involved citizen men exclusively — as politicians, representatives, magistrates, executives or voters. Wiki
So, it's not clear that Paul is speaking of the Mosaic Law, Christian Law, or Roman Law of the times. Most likely, unless someone can find otherwise, he speaks about the Roman law of his time.
TO ADD RE 1 Timothy 2:13, Eve was deceived, etc.
Paul begins the chapter asking for pray for those in authority (v1).
He then asserts he was sent to the Gentiles, first, before any other preacher (v7).
Men should pray (v8) and women should dress a certain way (v9). Is this followed today?
Anyway, why Paul? Adam, like Paul, came first. Women were deceived, who apparently were teaching something besides the pure gospel (1 Tim 1:3).
Can a woman be saved if she doesn't bear children (v15)? Of course, but what is Paul saying?
In his next letter, he praises Timothy's grandmother and mother who taught Timothy.
When I call to remembrance the unfeigned faith that is in thee, which dwelt first in thy grandmother Lois, and thy mother Eunice; and I am persuaded that in thee also. 2 Tim 1:5
First. Timothy's grandmother must have learned from the first Paul. Timothy was a gentile.
So, the books of Timothy are more about learning the truth first and then teaching that. We now have the whole Bible to help.