Not really sure what that means.
No. If you have the circuit properly configured, you should see very little variance on the collector current.
You probably need a lower value resistor between 'drive' and 'base' or the transistor can't turn fully on.
It also requires that the collector sits higher than the base so the supply voltage - voltage on your load is higher than the base.
Using a transistor as a constant current device works well if the voltage is high enough compared to the load.
I think you always have to do some experimentation regarding the base resistor as the Hfe has a large spread,
This is what I got: 3.8v / 61.2ma7.6v / 61.4ma11.8v/ 61.6ma