Can a person have a tooth infection without any pain instead my tooth has an infected smell when I floss?

Yes. Yes..Can have tooth infection and no pain if tooth is non vital..Yes can get smell when ossing if underlying periodontal disease..Gingivitis..Or not flossing regularly..Or poor oral hygiene.Cavities between the teeth.
Yes. When dental decay has not reach the dental pulp there is no symptoms of any kind other than bad odor from the cavity! see your dentist!
Yes. Depends on whal part harbours the infection, and what type of infection.