Q:

Can I use Free form to submit a calendar event in the front and post it the backend for all the events? 

Im trying to built a event calendar that uses free form to submit the event home page and then use the calendar.  So, if any wants to submit an event they can do so and then someone can go on the backed and approve the event. 

A:

If you would like user submissions to directly polulate the calendar, then you should use Channel Form and have users submit the events as entries in the calendar Channel. 
Assuming you are using Solspace Calendar, see the docs on Using with Channel Form. 
This same approach of using Channel Form holds true if you are displaying events using the native Calendar Tag, too (since those are also just Channel entries). 
If you absolutely need to use Freeform for your user event submissions and have them automatically become Channel entries, then you'll probably need to make an extension to convert the Freeform entries to Channel entries.