Is there a way to have it display the full line (in my case, 4,000 characters)
I don’t believe so, not currently.
There is an open issue regarding it, but so far it doesn’t appear to have had any action/traction: CLICK HERE
You might want to go there and state your opinion; adds weight for developers to make a change.
If I double-click on a line in the Find results window at position 2,500, the cursor jumps to the main window but at the location of the characters that were found, not iat the position I was in the Find results window.
Yes, double-clicking anywhere in the line jumps to the match point.