Say for example I have
A = (B) + C, I can't work out how to remove the parentheses/brackets around B without also deleting B. There's no way to select the brackets individually, as far as I can tell...
That behavior of Equation Editor is by design, and there is no way to delete B without deleting the parentheses. The program evaluates the parentheses as a whole object:
What you can do is (especially when the content in the parenthesis are longer) to double-click on the content to select it, and to use CTRL+X to cut it to be pasted later.