Using output variables within a strategy?

[KBJ]

Why does the "t" at the start of the variable name need to be small case while in the "public double" definition it can be capitalized?

This is because they are different variable names, for two different doubles. The property defines "The_ROC", whereas "the_ROC" should be defined in the "Variables" region of your indicator.

Take a look at almost ANY indicator provided with NinjaTrader or created by the wizard, and you will see this duality.

And other than that, you really do need to get some C# training or read a C# tutorial, there are lots of them on the Internet.