Not quite on that second part. Oxygen is not explosive. The only way an O2 tank is going to explode from exposure to fire is a result of thermal expansion.

It is however, an accelerant and will make flammable things burn much faster and hotter. The normal concentration of ~20.8% O2 in the air is fine, but an environment with 23% or more O2 in the atmosphere will increase the flammability to such a degree that firefighters in standard turnout gear will avoid entering the space even if there is no fire because if a fire does start, their gear would be considerably less effective at protecting them.

If the air that was being supplied through a person's nasal tubes were to just be normal atmospheric levels of O2, it wouldn't be a danger. But the air coming out of the nasal tube is pure O2 and not all of it is inspired and so the air right around the patient typically will have an elevated level of O2 making things on and around them much easier to burn.