the amnesty is supposed to be for tourists who became stuck here because of disruptions to air travel preventing their return home. i can't imagine there will be many who haven't managed to get a flight out with any amount of reasonable effort by the end of july.
There has never been any restriction on anyone (Thai or foreign) leaving Thailand. Whether they can enter another country depends on the border controls of that country.
If you mean teaching English as a foreign language I think you just need to look foreign and have a pulse. I met a headmistress of a Thai school once. She asked me if I thought I would be a good teacher. I said no. She offered me a job.
There is nothing "mysterious" about a few dozen people being infected with covid-19. China is just being extra careful to avoid the virus becoming a thing there again.