Stickers are always applied at a size relative to the screen. We've made a note to look at a future option to reset stickers to their natural size. A shadow toggle is something else we've had suggested for sticker sheets.
Currently, original placement of objects is done at a sub-pixel level if you're zoomed. However, if you place objects at 100% zoom, you can use the arrow keys to move the objects at pixel increments regardless of zoom ( 1 pixel increments or 10 pixel increments if you hold down the shift key )
Resident Bug-Hunter and Support Guy