Typically, once for you and once for your luggage. Once both are in the "secure" zone there is no reason for further inspections. However, if you or luggage leave the secure zone you or it will be re-inspected. For instance, if you fly domestic into SFO and have a connecting flight that departs from the international terminal you will have to leave one secure terminal and reinter going through another inspection. Further, if the airline accidently puts your bags on route to the carousel instead of transferring it to your connecting flight, your baggage will be inspected.

Been there, done that on both for SFO. Unfortunately, while I made my flight but 2 of 3 bags did not.

As for being present for your bags being inspected. You can request it but more often than not unless you are transporting a fire arm it ain't going to happen. Though there are three acceptable methods for inspecting a bag (hand, swab, x-ray) how a bag is inspected is not your choice.

To prevent the manhandling your best bet is to package everything in smaller compartments within your bags. That way they can inspect a smaller bag and put the content back in before going to the next one. For instance, for clothes we use Eagle Creek "Cubes". For other items padded bags or stuff sacs. Yes it is a PITA but then again having damaged personal affects is too.