A motor can fail in a mode which takes far more current than it normal operating currrent. Without a 3 amp fuse in the fan supply that over current will take out the fuse / MCB for the lighting circuit and thus put all the lights out.
When the fan is taking too much current ( fault or stalled rotor ) the 3 amp fuse will ( at least should ) blow before the 6 amp fuse / MCB protecting the lighting circuit and thus lights will still work.
Maybe but as I said the fuse is to protect the cable. Any protection for the fan motor must be provided internally by the manufacturer. It is quite likely these are sold in other countries where FCUs are non compliment and unavailable and where lighting is protected by a 16 amp MCB. Manufacturers MUST provide internal protection, probably a heat detector.