The small key probably turns the alarm on and off. Check under the bonnet -- you should see a dome-type horn in a rectangular box, usually just in front of the right-hand strut mount. There's a round plastic cap covering the key slot.
As for the fob, I'm looking for one myself. Mine (and possibly yours) is not the style where a chip is temporarily moved from the alarm unit to the fob to program it. It uses a removable module on the alarm controller (look under the rear seat) that is coded to the fob. As I understand it, they are sold as a unit.
Somewhere out there is a vast stockpile of fobs -- there must be, because they never seem to come with the cars.