not its not OK to have floating. connect it to GND

The polarity of the inputs to the feedback network isn't documented - need a + and - on that part

It's fundamental to the operation of BJTs (at room temperature). The collector current is ISexp(qVBE/kT - 1). kT/q is 26 mV at room temperature. IS will vary device to device, but the rest of the equation is fairly inviolable.

This is 'better' than R-2R -- use that topology, but just use single resistors in place of the 2R. Now (in the limit), the attenuation is approx 0.382/stage (½*(3-sqrt(5)), so 7 stages gets /1000, and uses 14 resistors (there are some approximations there).

It came up in a discussion with some colleagues about how resistor networks work.