Copper is not something that is calculated. The amount of copper might be, or copper losses / load losses, might be, but "copper" is not calculated.
Carbon is much stronger and because the motor commuter is spinning copper brushes will wear off quickly.
stick urwein in it
One thing you could do is look up the datasheet for the motor and/or contact the manufacturer of the motor. Also, if you know the guage of wire, you can calculate it based on the resistance of the coils on the motor/generator or on the coils of the transformer
A DC shunt motor is a motor using DC supply with the the inductor connected parallel to the armature.
6V dc motor
A synchronous motor is an ac motor that does not run on dc.
A DC motor will generate electricity, if used in reverse. IE, rotate it and electricity will be generated. The voltage will be dependant on the speed of rotation. The capacity (Amperage) will depend on the size of the windings and diameter of copper wire involved. Limitation to power and speed will also be limited by the construction of the commutator. All these variables are difficult to predict and unlikely a formula is available. You will need empirical means and careful testing, especially as the motor was not intended to be used in this way.
You need to find out if it's a DC or an AC motor. If it's DC you need to know if it's series, shunt or compound. If it's AC you have to know if it's a commutator motor, an induction motor or a synchronous motor. To calculate the performance, that depends what point you are starting from, in other words what data you already have available. The question is too big to answer without some initial guidance on these basics.
Yes it can and the otherway aroud a DC motor can be used as a dynamo
A dc series motor can work on dc and ac because dc motors are totally reversible.
for DC load and if its copper wire the cross section of the conductor wire is generally calculated as 1/4 th of the current rating . Eg for a DC load of 16 amp the copper conductor with 4 mm square is selected.
To state it simply, a DC brushless motor is not a DC motor. It is an AC motor with an inverter (or electronic commutator) on the front end to make the AC, so you can use a DC input.