I don't think the extra oil will hurt anything, but it could be a bit messy if it starts to blow out of the breather into the airbox. (more confusion?
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Best to drain it into a clean pan and put it back in to the proper level. Should be around 3.2-3.4 quarts with a full filter remaining on the bike. It'll take around 3.6-3.8 quarts with a filter change.
The oil cooler is the radiator looking thing between the front frame downtubes, just in front of the engine.
If you'll be doing some of your own maintenance, peruse the "tech vault", lots of good info there. If you don't find what you need, or don't understand what you do find, or need some clarification, just ask.
