Whenever you have a dialog up, the player loses "normal" controls; instead he gets a cursor, and his keypresses go into whatever control is up. So basically, he can't move around, shoot, or do anything while the dialog is up. I assume that is what you mean by "interfering with gameplay". Unfortunately there is no way around this.
I'm kind of unclear on what you want though, because how could you type stuff into a text box and play the game normally at the same time? Your character would move around while you try to type.... so I must not understand what you are asking.
Cut resources, however, look very similar to dialogs, and CAN be on the screen without interfering with the gameplay. Check out my tutorial on them
here. There is no way to "type stuff in to" a cut resource, though.