He's "invented":
A piano (unknown name)
A wake-up machine, which uses an alarm clock with a spool attached to a lever, attached to a feather, which tickes his nose and wakes him up.
A rain-making machine, but he kept punching it (but it wasn't going to work anyway.)
And "discovered":
A rabbit (or a "Poonga-Poonga")
A Snuffleupagus (or a "Shaggaphant")