In Checkers, can a non-kinged piece jump backwards as the second jump in a double jump?
This depends on the variation you're playing. A lot of variations allow capturing backwards with regular pieces (called men). The English variation is probably the most common that doesn't allow backwards capturing. By the international rules, capturing backwards is allowed (and mandatory if it results in the largest capture group).
There's an extensive list on Wikipedia, describing which variations allow backwards capturing by men, and which don't.
We grew up playing that the only time a non-king piece could go backwards is if the play was a multi-piece knockout and the the first opponet piece jumped was not a backward jump. So, if it was a three jump knockout, the first jump had to be forward but the 2nd or 3rd could be backwards