If you bought the ticket as a multi city ticket on one booking, you do not have to pass immigration. In case of seperate tickets you have to pass immigration, collect your luggage andere check in again.
even two border runs will be problematic if you extend them with 30 days. see replys to post of amy wang from june 7th. immigration has become though in recent years since the june last year.
Depends on your travel duration , some vaccines require a waiting period before they are considered optimally effective or require multiple shots with time between them
It immigration gets stricter and stricter in this , so I would be amazed if you would be allowed to do it a third time , there is a reason they are considering to reduce the visa exemption to 30 days