When dropping the pre-order bonus weapons such as the sawed-off shotgun - will I get them back every chapter? Or do I have to keep them the whole time if O ever want to use them later?
Most of the pre-order/DLC/booster-pack weapons can be purchased from some shops if (and only if) you have the booster-pack activated, so if you discard the one you are given you will be able to purchase another later.
The Wikia notes that for the double-barrel shotgun:
There is also a DB Shotgun on a high shelf inside one of the security stations outside at the docks.