Can I customise the columns on the 'Find Participants' page?
Yes, Its possible to alter the Columns in some search results of CiviCRM and definitely YES for participant search result.

You can create an extension and implement hook_civicrm_searchColumns hook. You can also find an example how to use the hook in the documentation.

Other alternate would be to create a report with same filters as Participant search but you won't be able to perform any action like how you can on participant search eg Update Participant status, Delete participants etc.

HTH

Pradeep