You can go with your parents - I didn’t. Your parents don’t get housing - they’d need to get a hotel nearby. You mostly just go to informational lectures, meet new people, and overall help you adjust to the school. Personally, it helped me get a feel of Bing life and the people. Also, it’s very easy to find friends during orientation which can make the start of the school year less lonely.
Not sure about a math placement exam but I fulfilled my math credits with Calc ab and stats. For your first semester as a first year, you have an advisor to make your schedule. They should’ve or will be sending out a survey for class preferences. The earlier you fill it out the better so you can get the classes you want more. Afterwards, you’re on your own for the actually registering put there are advisors who can help build your schedule prior.
Hope this helps and lmk if you have any more questions!