Is There a Way to "Thin" Wide Nostrils Without Doing Rhinoplasty?

Unfortunately, there is no "do it yourself" method for making the nostrils look smaller.  A full Rhinoplasty is usually not required for just narrowing the nostrils.  It may be possible to perform only an excision of excess nostril tissue under local anesthesia to give you the look you want.  However, it is very important to have a consultation with a rhinoplasty specialist for a full evaluation.  Often times the tip may have to be adjusted at the same time as the nostrils in order to have a balanced result. 

Yes, of course.  The best way to narrow your nostrils without surgery that I can think of is to get a piercing through both nostrils with a bar that traverses the nasal septum.  This will probably need to be custom designed so the screws and ornament are at just the proper length to narrow the nostrils the correct amount.  Surgery will be easier.

Nostril size is a fixed anatomic feature, and change to the nostrils generally require surgical intervention.  This is often done in conjunction with rhinoplasty surgery, but if done alone, can be performed in the office setting under local anesthesia.  Incision placement depends on the specific nature of the nostril enlargement, but generally these incisions hide well in natural anatomic landmarks.