The current flowing through the circuit, is it a constant 1 Amp, or does it depend on the load in the circuit..
The load resistance always dictates how much current will flow, in the classic ohms law formula current = volts/ohms, ohms of the load will determine the amount of current at any specific voltage, provided the voltage source can provide it. Batteries have 'internal resistance' which limit their maximum current flow capacity depending on the size and chemistry used for a specific cell or battery of cells.
I have a 32mA 6v motor connected to the supply. Should I limit the current flow to 32 mA or is it that the motor itself will draw only 32 mA from the supply??
The motor will draw what it requires. However how much current it draws will depend on the mechanical load placed on it. If yours draws 32ma with no load, try holding the armature fixed and see what the 'locked rotor' current draw is, much higher, no?
Lefty