a!pickerFieldRecords: opening the record on a NEW tab?

The link functionality appears to be automatic and unconfigurable. The only alternative idea I can think of off the top of my head would be to do a custom picker where you declare the item links yourself and wrap them in a!safeLink. AFAIK this would work, though it would take a lot more effort.

This is standard browser functionality. The user has the option to open the record in a new tab with CTRL + Click (or right click, open in new tab), but you are not forcing them to open a new tab.

Is there any way to make it not clickable?

What do you mean by not clickable?

I don't want the user clicking the link and leaving the task they were on. So I want to make the selectable item on the picker non-clickable.

again my best guess would be to use a custom picker field. it seems to me like some of these things should be controllable within parameters of a!pickerFieldRecords, but it looks like that's not the case.