Does anyone know of any downloadable chat bot that I can teach (i.e., that can record my definitions of things and repeat them in appropriate circumstances, and if I am lucky, say something new about it perhaps based on another different thing I have said)?

I understand your fascination: I suggest you play around with ideas for emulating intelligence yourself, as well as searching out any stuff in the public domain. Several years ago, I experimented with making bots on ActiveWorlds, but they had very, very rudimentary communications skills. You probably know about the classic Eliza program which made an attempt at passing the Turing test?

Is this the sort of thing you seek?