Question: Is there a way in Eclipse to easily find all appearances of a variable in a file without having to manually search (CTRL + F) for it?

Answer: 
with the cursor on the variable, press ctrl-shift-g. Works for variables, classes, methods, works across the entire project. If you just click on the variable, eclipse will highlight all uses of the variable in the current file, and mark the scrollbar with the places that are highlighted.
There is a search with many features accessible with `Control`+`G`, but it does not support variables inside of a function.

There is also another search, which occurs when you select a variable or other thing and press `Control`+`Shift`+`G`.