I just need to know two things.
1. Is there any way for me to make it so you have to apply to the website and be accepted before you can view the forums?
2. Is there any way for me to make an event calendar?

yes, set the view forum(s) to registered or create a rank for registered members and set view & reply for that rank.

Hello,

If you have further questions or concerns, please do open a ticket.

To answer your question, you can go to Admin Panel > Menu > Main Settings > Membership and Registration.

And yes, you can create event calendars by going to Admin Panel > Menu > Panel Layouts.