Are we allowed to reuse any code from a previous game
you can reuse any and all of the back-end functionality you want "Any templates, plug-ins and/or pre-builds will not count in the originality department" meaning that code used for handling in-game stats, physics or base AI would not really affect your score anyway because no one gives "originality points" for making a ball bounce or an enemy to walk in a straight line towards a target while avoiding obstacles.
but the front end: sprites, game mechanics, story, and so on - should be made during the jam or lose originality points.
might DQ if there is a massive abuse of that rule, but in most cases using sprites from the asset store or copying the plot of a book shouldn't be that bad as long as you give credit and take the point loss.
I wish that Jam hosts would acknowledge this fact a bit more.