When you do the node count, what exactly should you count? The number of nodes generated, including those not searched/stored in the transposition table? The number of nodes that are searched/stored in the transposition table? What is the common practice?

Typically you count the number of calls to the recursive search function(s).

I've always only counted leaves.

But you should know it doesn't matter what metric you use since there is very little cross-engine compatibility in how it's done. Node-count is primarily used to benchmark various hardwares testing your engine.