So do I!
There are two rotary methods of producing 3-phase from single.
A single-phase motor driving a separate 3-phase generator is called (not surprisingly) a motor-generator. The 3-phase output can be of high quality, but because all the power must be converted from electrical to mechanical and back again, such units are large, expensive and relatively inefficient. For example, to generate 10kW electrical output might require 12kW mechanical input to the generator, for which the driving motor might require 13.5kW electrical input. Other advantages of the M-G are the ability to change voltage and frequency (with suitable drivetrain) since the motor and generator are independent.
A cheaper, more compact and efficient method is to power a 3-phase induction machine, which can be a regular motor or a purpose-built machine, with a single-phase supply. Such a device is commonly called a phase-converter. With the aid of capacitors to provide the necessary leading reactive current it can regenerate the third line and provide a 3-phase output with the same line voltage and frequency as the single-phase input. Not all the power needs to be converted, and the fraction that does needs converting only once, hence the overall efficiency can be higher. However, since the output circuit is not symmetrical either for real or reactive power, the output voltage regulation and symmetry and the phase angles are less accurate and significantly load dependent, leading to higher losses and possibly reduced performance in the application load motors.
Regarding the driving torque, yes you are correct that the torque needed to drive a generator is proportional to the electrical load taken from it. The shaft of a 10kW generator delivering 10kW is 10 times stiffer to turn than when the same generator is supplying only 1kW (ignoring losses). It is not due to an increase in magnetic field (although in a real machine that does have to increase to compensate for increased losses). Rather it is due to the force on the conductors of the output winding cutting through the field, which is proportional to the current flowing through them. In a practical AC generator it is actually the field system that revolves while the output winding remains stationary, but the reaction force on the rotor creates the same effect of producing a torque at the input shaft opposing the rotation.