While the cursor is at either one of parentheses/brackets, pressing CTRL+SHIFT+] will select all contents in the parentheses/brackets. I will consider allowing this command to work while the cursor is at anywhere in the parentheses/brackets in future versions.
As for double quotes, there are no keyboard shortcuts, but you can select the contents inside the double quotes with a click of the mouse. To do this, go to Customize on the Tools menu, select the Active String page, select String enclosed by double quotation marks from the Type list, select Left Clicked from the Event list, and set the Select String before Action check box. Also, please go to Configuration Properties, Highlight (2) page, and ensure the Double Quotation Marks check box is set.