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.Did you go to Lists, New, and pick the table name from the dropdown under the Data tab?
yes.Do you have any existing Lists which use the same underlying table?
-- hugh