How long does bad breath associated with nasal foreign body last?

Very short-lived . It should not last very long after removal, unless you've developed a sinus infection from it. Try a neti-pot or sinus rinses twice a day for 3 days, if not gone by then go see a nose and sinus specialist.
Until Infection Heal. Metallic taste from a nasal foreign object is either from the object chemically reacting with the nasal mucosa or causing an infection. Normal taste should return in 3-7 after the object is removed and the local infection is healed.

Related Questions

How to prevent foreign body inhalation in cases of nasal foreign body.?

Nasal foreign body. Assuming you have a foreign body in the nose, the foremost strategy would be to remove the foreign body. Your nose will be much happier that way, too. If the foreign body can't be taken out right away, avoid sleeping on your back, breath with your mouth open and expedite getting it out. Removal of nasal foreign bodies is typically not something that should wait...Not even longer than a day. Read more...
Nasal foreign body. I think you should make an appointment with an ent. In my experience, many primary care physicians and emergency room physicians don't do this often, and may push it further in as they rarely have the correct tools. Read more...

Could a very small nasal foreign body that pushed thru somewhere in the cavity cause endocarditis?

Question unclear. Anything that places bacteria in the bloodstream, particularly if the organism has a high pathogenic potential, creates a risk of endocarditis, but this often requires the presence of some pre-existing cardiac condition that creates a risk. It is doubtful that what you describe will cause endocarditis, but have no idea what "pushed thru somewhere in the cavity" means. Elucidate. Read more...
Anything's possible. However, there is too much missing information for a good answer. If you have a normal heart, the chances are very, very small. If you have a known heart problem, then there is a slight chance. There is sort of an assumption in the question that endocarditis has already been confirmed and you are looking for the potential source. More must be known for a reassuring answer either way. Read more...