With the Square online store the only way to do this is to add locations in your Square account.  This will allow you to control and sell the inventory at your event and online.  This is like creating a new store in your account so some things you do will be based on the location and some will be based on your account.  You can have the same item in every location but Inventory for example will be based on the location.  You will be able to see reports for everything and for each location or for you each event.   Note that when you log into the Square app you will have to pick a location you want to sell from.  You have to sign out and back in again to change locations.

Your online stores will be seperate and cannot be connected via square but can be connected with your own website.

Hope that helps.