As regards the vents required in the cupboard, assuming the boiler
is a room sealed appliance there may be no need to have vents to
outside, refer to manufacturers instructions for guidance before cutting
into your walls.
Open vented appliances require ventilation (air) for combustion, a lack of
air would mean the generation of carbon-monoxide and serious health concerns (even death)
A room sealed balanced flued appliance (most modern ones are this!) may
or may not require ventilation depending on the appliance and the type of
cupboard it is installed in as this ventilation is only required to dissipate heat and remove condensation (again refer to manufacturers instructions) and it
may be possible to provide this ventilation from the room (via a vent(s) in the cupboard) rather than to outside (assuming the all knowing builder installed the correct room vents to regulation!)
Room sealed balanced flued appliances take combustion air DIRECTLY from outside via the air intake on the flue, and are generally considered a safer appliance via this design.
Compartment ventilation is usually done with 2 vents not one, one at high level, one at low level, as per manufacturers instructions bases on the kw input of the appliance, both vents must be on the same outer wall or communicate with the same interior room (not a bathroom, bedroom, shower room or bedsitting room) and must also be labelled with the correct warning labels.
Once this installation is complete the gas installer is required to issue you with a 'Declaration of Conformance' for the installation (this will include signing of on any ventilation requirements)
Also, as this is in your living room, is there also a gas fire, and if so, is the ventilation for this provided also.