The "Son of" surnames

Governments needed a stable way to track people across generations, so most regions eventually required families to keep one surname for good. Rolling patronymics made tax rolls, census counts, and land registers unworkable once a name reset with every child. Wales, parts of Scandinavia, and other regions fixed this through law over the following centuries.

Yes. Iceland still uses a fully patronymic system today, so a person's last name is built from their father's first name and changes every generation instead of being passed down as a fixed family name. Most other countries dropped this practice centuries ago in favour of permanent surnames.

Yes, many patronymic systems use entirely different endings for sons and daughters. Icelandic marks a son with -son and a daughter with -dóttir, Welsh once used ap for son and ferch for daughter, and Arabic still distinguishes ibn from bint. English lost that split once surnames like Johnson became fixed for everyone.

No, not necessarily. Patronymic surnames form from a father's given name, so unrelated families can end up sharing one just because two different fathers happened to share a common first name like John or Peter. A matching surname alone does not prove any real family connection.