What can happen if I have 18'' at the rear and I use 16 or 15 at the front with ET Street Radials?

 

If the are the same overall diameter it will be fine, if not then you can through the traction control off which will really suck if you're trying for track times. Also you're probably best going with a 16" because the vast majority of 15" wheels do not clear the brake assembly.

 

I would put on the stock wheels on the rear, if you still have them. More than likely they are lighter than the 18s. Also over-inflate the rears for less rolling resistance.