Their relationship with the local law was important in the book of 1st Corinthians. For example, wives wearing headcoverings was a roman law, Men not wearing headcoverings in religious worship was also important relative to the cultureal meaning. The brother sleeping with his father's wife was in violation of roman law, and the membership of the ecclesia was in violation of roman law for not reporting it.
Paul was very muich concerned with Christians not causing trouble.
Yes.
See Adam Clarke's commentary on 1 Tim 2:12
Verse 12. Nor to usurp authority] A woman should attempt nothing, either in public or private, that belongs to man as his peculiar function. This was prohibited by the Roman laws: In multis juris nostri articulis deterior est conditio foeminarum quam masculorun,; l. 9, PAP. LIB. 31, QUAEST. Foeminoe ab omnibus officiis civilibus vel publicis remotae sunt; et ideo nec judicis esse possunt, nec magistratum gerere, nec postulare, nec pro alio invenire, nec procuratores existere; l. 2, de Reg. Juris. ULP. LIB. i. AD SAB.-Vid. POTH. Pand. Justin., vol. i. p. 13.
"In our laws the condition of women is, in many respects, worse than that of men. Women are precluded from all public offices; therefore they cannot be judges, nor execute the function of magistrates; they cannot sue, plead, nor act in any case, as proxies. They were under many other disabilities, which may be seen in different places of the Pandects.
But to be in silence.] It was lawful for men in public assemblies to ask questions, or even interrupt the speaker when there was any matter in his speech which they did not understand; but this liberty was not granted to women. See the note on 1 Corinthians 14:34; 1 Corinthians 14:35.
As to whether the verses are a scribal insertion, here is a place to begin your research. Go where you wish from there.
https://hermeneutics.stackexchange....orinthians-1433-35-an-interpolation/1158#1158