In a Ce transistor, why does an increase in voltage between (collector and emitter) affects voltage between (collector and base) but not Voltage between (base and emitter)?
The collector base junction is reverse biased therefore, an increasing collector voltage has minimal change on the voltage between base and emitter.
This is because the B-E region is forward biased and exhibits a "stiff" impedance electrically. This makes it not susceptible to the extra few nano amps that arise from the increase in voltage across the reverse biased collector-base junction.
If you increase V1 then the voltage Vce will also increase. The voltage Vbe can only vary a very little bit. For now see it as stable at 0,6V. That makes Vcb = Vce - 0,6V. Therefore if Vce increases then Vcb increases as well. The increase of Vce and Ib is therefore a result of increasing V1.