Is there a way so the Edit Hyperlink box always opens on the 'Place in This Document' section?

As far as I know, you can't control Word's behavior when you open a dialog box.

Sometimes -- but not always -- when a dialog box refuses to cooperate, you can beat it into submission with the SendKeys command in a macro. This acts as if you're hitting keys on the keyboard, and lets you (try to) use the accelerators, the underlined letters on buttons.

This macro (see http://www.gmayor.com/installing_macro.htm if needed) works for two out of the three ways of opening the Insert > Hyperlink dialog:

Sub InsertHyperlink()
    SendKeys "%a": Dialogs(wdDialogInsertHyperlink).Show
End Sub

The specific macro name InsertHyperlink causes it to run instead of the built-in command. It puts the Alt+a keystroke into the keyboard buffer and then displays the dialog. I find that the accelerator works correctly if I click the Hyperlink button on the Insert ribbon, or if I put a button on the Quick Access Toolbar that runs the macro. However, if I use the keyboard shortcut Ctrl+K to invoke the command, the dialog displays but ignores the SendKeys (although pressing Alt+a after the dialog appears does work).