Okay, sorry for more questions but I want to make sure I understand before I send you some ideas and docs.
Every user who visits the site should see the same options?
OR
User 1 visits the site and picks item 1. User 2 visits the site and should not see item 1 as an option bc user 1 already picked it.
And yes - you can add any element you want as far as selection is concerned. To add a checkbox to the repeater drag the element over your repeater element and you will see “Attach to Item”
Then in the code on submit, you can use the dataset API to remove the selected item
Here is the link to the Wix Dataset API