Do vaccinated people shed spike proteins or the virus could be harmful to others?

The short answer: no.

The COVID-19 vaccines approved for use do not contain live virus, and thus it is not possible for any “viral shedding” to occur.

Viral shedding is theoretically possible only for vaccines that contain a weakened live virus, though it is extremely rare for this to infect someone else with that virus. COVID-19 vaccines do not contain any live virus, and thus the vaccine cannot result in anything being shed that could infect or harm others.