1. The book does not specify the exact model of relay to be used, merely that it should be within certain specifications. The designer appears to have assumed that no resistor is necessary in series with the relay coil. Is this a valid assumption?
A relay coil has its own internal resistance due to the size and length of the wire in the coil; the relay manufacturer designs the relay so this resistance provides the proper operating current at the relay's intended coil operating voltage (5V, 12V, 24V, etc.). So yes, it's a valid assumption-- unless your supply voltage is higher than the relay's coil rating, in which case you'll have to add external resistance.
2. Is there a special name given to the diode?
I've always referred to it as a "catch diode."
3. My understanding is that the diode wastes any current that is induced by the relay coil after the transistor is switched off. Is that correct?
More or less, although it doesn't "waste" the current but rather provides a path for it after the transistor is switched off and until the energy stored in the relay coil's inductance is eventually dissipated.
4. Is there a special name for the 6.8 kohm resistor? What is its function? Is it necessary?
I've never seen a name for it, but it's mainly there to ensure the transistor can turn off by providing a path for any collector-base leakage current. It may be necessary (for instance, if the device is being operated in a high-temperature environment) or it may not; it's there as cheap insurance.
5. If I read the book "The Art of Electronics", will all this become clear to me? (Heh, heh. I've had that book recommended, but the investment is not trivial.)
Oh, yes. Plunk down the hundred bucks for that book and read it, and you'll understand everything-- electronics, the meaning of life, the ultimate fate of the Universe, and probably even how to mix a first-class Martini.
Seriously, it's a good book and in my opinion well worth the $$$ if you're really serious about learning electronics.