If a person undergoes an emergency baptism, then recovers, do they need a "non-emergency" baptism? If a person receives an emergency baptism, but then recovers from that danger, is that considered valid for the rest of their life? Or would they be expected to undergo a "non-emergency" baptism in the future?

In other words, is emergency baptism temporary or is it permanent?
A baptism is a baptism. There is no such thing as a "temporary baptism".

The key part of the Canons is as follows:


  An infant in danger of death is to be baptized without delay. (Canon 867 §2)


There is no provision for any kind of "rebaptism" or anything similar: indeed "only [a person not yet baptized] is capable of baptism" (Canon 864).

There are other rules about baptisms in case of necessity (imminent danger of death being the most common necessity). For instance, any person with the correct intent may baptize in necessity, not only a priest. None of these rules, however, suggest the emergency baptism is anything other than full, complete and efficacious.