Input resistor to BJT base > ground resistor, why?
Resistor-Transistor logic is mostly dead these days.  Anyway, your observation is correct, and there will be some static power loss there, but the analysis is more concerned with voltage levels than currents.

In logic, transistors are conceptually treated as voltage switches, not current multipliers.

To allow the designer to mentally keep track of a large amount of logic, he tends to work with blocks corresponding to logic gates, not individual transistors and resistors.  R5 is, along with R3, R4, Q2, and Q3, part of an AND gate.  R6 is part of an OR gate along with R7, R8, Q4, and Q5.  No one bothered to perform optimization of component values across adjacent stages -- the only consideration given to the resistor values will be to make the input impedance much higher than the output impedance of the previous stage, whether or not that is actually needed.

By using gate-level circuit blocks, the designer only has to verify that each gate functions correctly for the various local input voltages.  If he tries to optimize across the entire circuit, significant static power savings could be achieved, but the load currents may depend on additional signals and the complexity of the analysis grows exponentially.

TTL and CMOS logic families improve considerably on the behavior causing you concern, because the pull-down is built with a transistor as well and able to switch open when not needed, thus minimizing waste current.