From the problems that you are having I recommend that you do the following:
First, work with layers and folders. It really does help, Group individual sprites together in folders so that you can move the whole of them around and parts that are replicated should exist on seperate layers.
(So if there is a sword or something it should be on a layer, eyes should be on a layer, etc). Thats where the real power of these type of applications are for such a task. If you mess something up, you don't mess it all up just that layer.
Then, enable the ruler and enable the grid. (Also take the time to set them up correctly in the preferences menu). If click the ruler and drag away from it, you can create guidelines. Setting up your own limits using the guidelines will allow you to snap the sprites (which should now be in folders) to the grid lines allowing you to position them far better.
Then finally, if things still seem a bit out of phase when the animation is playing. If you zoom all the way in (you may need to make sure this is enabled in the preferences menu) you can see an individual per-pixel grid. Which should allow you to place things exactly where you need them to be.