access denied on member signup with civicrm for anonymous
The "event registration" link you give isn't the public-facing event registration page, which is why you're getting "Access Denied".  The page you're linking to is intended for staff to add event registrations on the back end.  The public-facing page will be: https://hebrewburialofnewhaven.org/civicrm/event/info?reset=1&amp;id=1.  When I go, it says that online registration hasn't been enabled for this event.  You'll need to go to CiviCRM Events menu » Manage Events, then click Configure » Online Registration next to the test event.  Check the Allow Online Registration checkbox and save the event.

The error on the contribution page isn't as obvious to me - but if you didn't change the default permissions for CiviCRM, then it's a configuration issue on the contribution page itself.

If you still need help, questions like this are well-suited to chat: https://chat.civicrm.org, in either ~town-square or ~user-support channels.