Is a valid B1/B2 visa cancelled if an F1 visa is refused?

While the B1/B2 continues to be valid, an entry with that visa is likely to subject you to questioning at the border. Customs and Border Patrol (CBP) has access to the shared database and can see the F1 refusal as well as the consular official's notes on why it was not approved.

Depending on circumstances, attempting to enter with the B1/B2 could result in a refused entry and, perhaps, invalidation of the visa. You would have to present convincing evidence that you have no intentions of studying in the US, that you are just visiting, and that you have concrete plans and significant reasons to return home. Should you successfully enter on the B1/B2, don't make the mistake of then applying to change status to F1; the refusal is on record, and such an action could call into question your current, and any future, visas.

As far as the notation about your passport, it's simply that, nothing more, showing the document location, at the Consulate, before it being returned to you.

It depends on whether the consulate cancels the B1/B2 visa when you go into apply for an F1 visa. Consulates sometimes cancel existing visas when you go in to apply for a visa (before you know whether you are approved or denied for the visa you are applying for), although I am not sure whether they would do so for a B1/B2 and F1 case.