I know that a flywheel is used to provide inertia. Do motorcycles have them? If not, why don't they have it?
A flywheel is used to even out impulse, and to store energy (these are both the same thing in reality)
An engine, especially when running slowly (such as when starting) has relatively large impulses from each cylinder firing, but without a flywheel there is very little to keep the crankshaft turning once the sparkplug had fitted and expanded the mixture in a cylinder.
What the flywheel does is store up the energy of that explosion in rotational energy, driving the crankshaft round to the position for the next explosion, and so on.
Yes, a heavier mass flywheel takes more energy to move, but it also keeps moving longer so there are pros and cons.
A dual mass flywheel typically has two flywheels, one of which can be declutched and disconnected when not needed (ie when under light load, moving at speed)