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In your first schematic, Figure 1, R1 and R2 are not necessary if you have picked appropriate values for V+, V- and RE. The voltages and RE would determine the bias for the transistor. If you were not able to provide appropriate voltages or if you wanted to be more assured of setting the bias point more precisely where you want it, then you would use the voltage divider network of R1 and R2.
Notice that in your second schematic, Figure 2.6, the emitter of the transistor is tied to ground. As noted in the text above your figure it says “returning the emitter resistor to a negative supply voltage, you can permit negative voltage swings as well.” What they are pointing out is that a negative going signal on your input would not produce any output unless you connect your emitter resistor to a negative voltage.
And your last question, “What is Rin and Rout?”, should use lowercase R as shown in the schematic. r in and r out are the AC input resistance and the AC output resistance of the circuit which are more commonly referred to as input impedance and output impedance.
I hope this helps to clear up some things for you.