Hi lesha64,
Welcome to Apple Support Communities!
I see that you have an issue with being able to invite contacts to an event in Calendar. To make sure that you are covering all the steps, this article has more information on how to do that: Add and delete reminder lists on iCloud.com - Apple Support
If you still have an issue after following those steps, I would recommend some basic troubleshooting such as restarting your iPhone. Here’s how to: Restart your iPhone - Apple Support
Hope that helps. Reach out with any questions.
Have a great day!