Hi Linda,
Thanks for reaching out! These are great questions.
The short answer is yes to all of those things, except for the very last one. Community Events can handle the featured images, events being published to your calendar and categories being selected during submission.
What is cannot do is charge a fee for event submissions. You might, however, want to look into Restrict Content Pro as a way to make that happen though. You could use it to add a paywall before anyone is allowed to access the event submission form.
Does this help answer your question? Please let me know. 🙂
Cheers!
Geoff