Vmd is velocity for minimum drag. I know not of Vimd, perhaps a typo.
An jet/turboprop best range is theoretically approximately 1.32 * Vmd (actually the fourth root of 3, then multiply by Vmd, if I remember correctly). This assumes a constant fuel flow and thrust as speed changes, which may be close for jet engines, less so though for turboprops.
Further, this assumes zero compressibility drag, so for jets at mid to high altitudes, this can be wildly inaccurate. Take for example an 777 at cruise altitude, I'm guessing Vmd to be .75 to .80 depending on weight. Multiply by 1.32 and you get best range to be M1.0 or greater, clearly impossible. But low altitude for jets and turboprops, I expect 1.32 * Vmd to be fairly accurate.
Intruder, I'm wrestling with whether your answer to question #4 is correct, that Thrust SFC ** AND ** fuel flow will both decrease. I'm taking TSFC as lbs of fuel consumed, per lb of thrust produced, per hour of flight (or metric equivalent). Higher altitudes should increase TSFC, as a jet engines has it's lowest (or best) TSFC at sea level. The question is not that clear on specifics which makes it difficult to answer too. Of course, I could be wrong...
Hawk