Should Karr have to reimburse the government for the plane ride from Thailand, since he was not charged?

I think that's EXACTLY what he did. He was about to get nailed by the police in Thailand (the prisons in Thailand make the U.S. prisons look like sunday school!). He popped the confession to get his worthless carcass out of there.

I think he should be forced to pay EVERY penny back to the government.

Karr probably won't have to pay the government (a pity...), but I think he used the confession of killing JonBennet to get out of Thialand because maybe their jails over there aren't very nice. Seriously, some countries don't take care of the people that they lock up and it's up to their families to provide food and the like to keep them alive. I think Karr was just trying to get back to better living conditions in the U.S.

Maybe he even wanted to be famous for her murder.

absolutely he knew he would have had it worse in Thailand which is why he confessed, maybe an extra sentence when he finally does get charged for the pornography

the extradition was based on shotty dna. not so much is confession. He is a known idiot so the DA was skeptical of the confession from the beginning.

The DA is gonna have to foot the bill. sucks but thats how its gonna work.

should karr sue the government for false arrest?

yes he should and he should be returned to thailand if he is in trouble

yes

Sure. Why not.