You will always need to edit the precise details of your drawing in Visio, because the options for modifying color, fonts, and backgrounds of the Visio drawing in Word are limited. Only the basic options on the Picture toolbar are available, such as resizing, positioning, cropping, and adding borders.
Once you have your drawing where and how you want it, you can lock it in place so that it stays where you put it. Text will move around it as you type—rather than the drawing moving with the text.
To detach the picture (or object) from the text, use the options in the Advanced Layout dialog box. You'll see how in the practice session.