Paul Galesko is not handing Columbo anything. He is in fact being his own arrogant self and by doing so, he gets caught Galesko thought that he would never get caught.

Findlay Crawford was arrogant because he asked Columbo if he could put him in a prison where they will need a conductor for an orchestra.

A reversal on this might be when Columbo brings along a dessert wine to share with Adrian Carsini when he corners him.

Carsini knew it was over the second his secretary confronted him.

Short Fuse always makes me wonder if Columbo has a trophy case for the crimes he's solved like Batman has in his Batcave.

What do you mean by Short Fuse? The cigars and cigar box?