Hello Alexander,
Without knowing the age, make and model of fire fitted, it is difficult to give specific advice, however, it is not difficult to check if any screws are loose, and it does not need to be a dealer to do this provided you can get to the back of the fire without removing it.
If the fan is vibrating excessively, then it suggests the fan is out of balance. It is a natural effect for the fan to collect quite a lot of dust, and they do need periodic cleaning. Sometimes the collection of dust can impair the balance and cause it to vibrate more.
In general, the Carver and Truma fires allow the user to remove the front panel, and this allows some access to the fan for cleaning with a vacuum cleaner. - see your users handbook for details.
If you are not sure about attempting this then refer the job to a competent fitter.