Power MOSFETs have [relatively] very high gate capacitance.
For simple on-off switching & moderate loads, that probably does not matter; the FET may take a millisecond or a few milliseconds to change between fully on and completely off.
During the part on / part off stage, it will dissipate rather more power than in the on or off state.
As long as that burst of power (and heat) is not excessive, it's not a problem.
But, if you are trying to switch a MOSFET very quickly & repeatedly like with PWM or in a switch mode PSU, or with high loads, the change between on and off must be as short as possible, to properly control the load and minimise the power loss and FET heating.
That's when high current gate drivers come in, that can often give current of an amp or two, to charge and discharge the gate as fast as possible.
A "Flyback" or "flywheel diode" is just a type of use of a general purpose or fast recovery diode - when it's used with an inductive load to prevent high voltage spikes damaging things or causing electrical interference; or when deliberately to capture the energy from the inductor, as in a power supply or converter.
A TVS is rather like a zener diode but faster, it will conduct and dissipate the energy from an overvoltage spike.
(Voltage-dependant resistors, aka VDRs or Zenamics are another type of device that does a similar kind of thing).
A resistor can be used across an inductor to limit the back EMF spike, as it will draw current in proportion to the voltage so limit it; eg. if it takes 1/10th the inductor current at normal voltage, it will take the full current at 10x voltage so the spike cannot be any higher than that.
The back EMF spike from even such as a small 12V relay can easily reach 500 - 1000V, so even limiting it to a few times working voltage can help prevent the switch or contacts controlling it from arcing or being burned.
Resistors across large coils like magnetic clutches were common in older machines, before semiconductor devices were developed & are sometimes still used, as they damp the circulating current far faster than a flywheel diode, allowing the device to switch off more quickly.