Does anyone know what a 1951 Australian half-penny would be worth if anything? I also have a 10 shilling (Australian) bank note in excellent condition but don't know the year.

There are five different types of 1951 halfpenny so it depends. Similar thing with 10 shilling notes - they were issued from 1913 until some time in the early 1960s (I'm not sure when the last run was exactly) and again there were a few different designs.
If you've got some images that would help.