Many of your questions have no firm requirement. It may be up to the individual country requirements and the type of service that you will provide.
1. If you do not transmit this tone to the FXS, then how will the FXS user know there is another incoming call and switch to it? In many countries, like the US, you pay extra for the call waiting feature, but if you do not transmit this through, then you are basically denying the user of a feature they paid for.
2. Again, this may be a feature that the user paid for on the PSTN line and you should send this through.
3. You stated that a “PSTN user” wants to call another voip user, but keep in mind call waiting is for the FXS user, not FXO user.