1. You can stay in the US indefinitely, as long as you are going to school/etc. Since you are going to graduate school, your visa remains valid. It will remain valid beyond 2021, as long as you are going to school. Beyond 2021, if you leave the country, you need to re-apply for a new visa. IF you don't leave the country, you can continue using your visa as long as you are going to school.
2. You can go back home and come back with the same visa, as long as it is not expired. They will demand a new I-20 when you try to enter the US, so make sure you have the new I-20 before you leave.
