Voltage Divider Configuration of Transistor
If you were going to do what you proposed in Figure 2, then why bother with the divider at all? Just use a resistor connected to +V with the appropriate value to produce the desired bias base current.

But this is BIASING, not just sending a lone current through the base-emitter. Biasing implies you might end up having another signal ride on top of (superimposed onto) the bias current something (i.e. using a DC-blocking capacitor to couple an AC signal onto your bias current). A series resistor like Rb will muck that up. This is why you don't want anything resembling a series resistor like Rb there.

To directly answer question #1:
The voltage across base-emitter won't a diode junction of exactly 0.7V (and neither will your resistors) so that won't work in real life. You're probably more interested in the current flowing through the base-emitter junction anyways than the voltage across it. With a diode in the base-emitter junction, little changes in voltage make huge changes in current so it's not really a good way to try and control the voltage across the junction when you're interested in the current. 

Using a divider with Thevnin to analyze it lets you come at it from the perspective of current through the base-emitter while not actually having a series base resistor which would interfere with any AC coupling you might attempt.

My analog knowledge is not well-developed and very rusty, but I think that's pretty much the gist of it.