Do electrons truly flow in circuit?
The key here is the concept of metallic bonding. or, the sharing of electrons between metal atoms like those in a copper wire (a typical conductor). In this type of atomic bond, electrons no longer belong to one atom or another; they're shared equally amongst all atoms.  As such, one electron truly does go bouncing around between the atoms in the direction of the electric current.  

One atom is close enough to another in metallic-bonded substances that an electron is attracted just as much to one nucleus as the next one over, so it's not so "illogical" to think that an electron might "break free" of its original nucleus.  

Chemical reactions occur between atoms, not electrons, and atoms in a metal are already metallic-bonded together, so a few stray electrons wouldn't do anything to create new reactions.  However, the electrons do behave oddly!  That's the beauty of metal conductors: their electrons are free to flow wherever an electric or magnetic field dictates, meaning that they can do some pretty cool things!  

The nuclei of a conductor don't become ions because every time one electron leaves, another takes its place.  Think of people at a gas station on a busy day: every time one car fills up and leaves, another pulls in almost immediately.  Thus, the metal atoms never have time to become ions, because there's plenty of electrons to keep them company.  

As (nearly) always, Wikipedia has a bunch of information on the subject.