Do you have to apply and get into ALL graduate programs?

I have never encountered a graduate program that just takes anyone who is interested.  There are minimum admissions criteria and application requirements.  There are programs who accept a lot of applicants, but there are many that accept very few.

No, of course not. That would be ridiculous. You apply for admission to graduate degree programs offered by various graduate colleges and universities AND various departments and schools. . That includes law school. medical school, veterinary school, public health graduate. 

No, you do NOT get into graduate school just because you are about to get or already have a bachelors degree. 

You must apply for admission to graduate schools, just like you applied for admission to university for bachelor's degree program. Each school sets its own requirements to apply for admission. See the schools' websites for complete details on admission requirements, application procedures, application fees, etc.

You must apply for any graduate program and meet all the requirements, and still you may be rejected based on any number of factors.

No! You apply for the program you’re interested in and only that one.