I am unable to comply with the immunization requirements of U.S. universities due to my religious views. Probably not - universities usually try to accommodate religious objections to immunizations, as well as other religious needs of students. Contact the university admissions office before you apply. My university has a lottery for on-campus housing. You should arrive at least two weeks before classes begin to find housing.
Some universities can provide temporary accommodations for international students.
If not, you will have to find somewhere to stay when you first arrive. Hotels are often expensive. Ask your International Student Advisor or Housing Office staff about which neighborhoods are best to live in and if there are any neighborhoods you should avoid. If you will be using public transportation to get home, check the time of the last bus or subway train. Your local police department may be able to give you advice on suitable locks and security measures for your doors and windows.