I accepted paid internship in Japan (Meti) if i get full time job offer from that company after internship Can i go back to my home country for visa or stay in japan?

I accepted paid internship in Japan (Meti) if i get full time job offer from that company after internship Can i go back to my home country for visa or stay japan?

And I want to also known if i get offer can i immediately start work or should i wait until April some people mention job in japan start at april is it true?

Thank you.