What would be a reason to do a tracheostomy?

Varies. Mechanical obstruction of the airway is one (e.g. Tumor, swelling). The other common one is patients on long term ventilator support (respirator) who may benefit from better clearing of secretions and earlier liberation from the ventilator.
Several. The indications for a tracheostomy are: upper airway obstruction, chronic aspiration, prolonged ventilator dependence, severe obstructive sleep apnea, and surgical access.