Custom Search Criteria

Hi for All at the beginning,
I would like to search incidents and incidents reports by parameters no available in default Build Search (e.g. Resolution Classification or Reaction Time - Time of Take a ticket - Time of creation ticket). I can’t find a way to add new search criteria to Build Search section. Could someone try to explain me method how can I do this?

I think, you should create CustoField ReactionTime and create action to add value in this field when ticket is taken. Then you can make search by this field

How can I insert current time of transaction to the custom field when user takes a ticket? I know that I should create a custom action and condition but I don’t know how.
How can I search in Build Search section by my custom fields (right now my fields are invisible in this section)?

EDIT: I figured out condition when ticket is taken and now my scrip send a mail to requestor when ticket is taken.
I don’t know how to set current date and time as Custom Field value and how to run scrip only one time (when first take occur)? Right now, when one RT user set Nobody as ticket owner and another user pick up this ticket condition occurs again. How to avoid this?

According to RT Docs - Customizing/Search result columns I already added column Reaction Time to Search Results, but when I try to sort by this column I receive blank report (no tickets found). When I sort again e.g. by ticket id records are visible again. How can I make my custom search column sortable?