[plt-scheme] instantiating another instance of same class

Is there a way to do any of the following with the object system
(in decreasing order of generality)?

  1. Procedure that accepts an object instance and returns the object
     class.

  2. Way to get the most specific class of an instance from within a
     method of the instance.

  3. Way from within a method to make a new instance of the instance's
     class, with specified init fields.

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