Can constant pressure on the cartilage of one's nose over a extended period of time alter its shape permanently?

Not feasible option: It might be possible, but probably not in a desirable fashion. Downward pressure on the nasal tip might eventually drop the height of the nasal tip, but that would take a very long time & come at the cost of septal deviation and nasal airway obstruction. In order to reshape the nose, rhinoplasty is usually the answer. Sometimes "injection" rhinoplasty is possible. Seek a qualified surgeon.

Yes: Cartilage can be altered be trauma and pressure from many sources or causes.

Yes: Yes, but you will not resolve a large bump by pressure!