1.) Definition of saturation: The voltage drop across the collector resistor (caused by the collector current Ic) must be large enough to make Vb>Vc. That means: The base-collector-junction now is forward biased. As a consequence - the base current Ib will be much larger than expected for linear operation because now there will be an additional current through the forward biased B-C junction.
How do we know if the transistor is in saturation? As a good indication for this state we require that the base current Ib is app 10% (rule of thumb) of the collector current (B=Ic/Ib<10). Therefore, we use a base resistor Rb in series with the switching voltage Vs that allows such a large base current Ib>0.1*Ic.
Therefore: Rb=(Vs-0.7)/Ib. The minimum required collector current Ic results, of course, from the resistor Rc and the supply voltage Vcc.
2.) With a collector resistor as low as 1mOhm you hardly would be able to create a voltage Vc at the collector node which is smaller than the base voltage Vb (as required for saturation).
3.) This question was answered under 1.).
