I am new to SharePoint and I changed the event content type at the parent level. Now existing calendars list content types groups are _Hidden. The calendars also do not work now. Is there a way to re associate the child to the parent without losing the data already in the lists?
Rule #1: never change an out of the box SharePoint element.
Instead create a copy and change that. In this case, create a new content custom content type based on events and modify the custom content type.
You don't provide enough information to give concrete advice, but you can use the browser interface to move the content types out of the _Hidden back into their previous groups. Start with the content type you can still see and then click the link to its respective parent content type, until you get to the hidden one.