For running J!5.1 you must https://fabrikar.com/forums/index.php?wiki/update-from-github/ or include the new file manually https://fabrikar.com/forums/index.php?threads/joomla-5-1-and-fabrik-cannot-find-files-error.54473/post-285151 See also Announcements
Please see our announcement here.
Yes, sure, but that's not a project to be explained in 2 or 3 lines.Someone can help me?
So yes, try the fullcalendar.
But it doesn't have a "year view" (if this a critical point in your case).