I need to change my security questions for iCloud because I cannot remember them but it refuses to let me. I just got a new Mac and in order to set anything up, I need to get into my iCloud. Im thinking about setting up a new Apple ID?

If you can’t reset the questions yourself contact Support in the country where you are (and which is therefore the country on your account) and see if they can reset them for you : Contact Apple for help with Apple ID account security

If your country isn't on that page try this form to contact Support : https://www.apple.com/emea/support/itunes/contact.html

(If you do create a new account, anything downloaded by the old account is permanently tied to that account, so only that account can authorise its purchases on a new computer, potentially redownload them from the store, and download updates to its apps.)