SpikeTV pays TNA money for original content, TNA's international deals are basicly reruns of the show. So they cant air the show live, even if they want to. It works different for PPVs though, a PPV can air live in other countries (i think India aired BFG live recently).They could broadcast it live easily.
All they show during the night are old game shows.
Very good idea, TNA would really benefit moving to FX. If its already popular on challenge it will be so much popular on FX.They should really try and get it on FX, imagine the ratings boost considering Family Guy would be on before it, plus family guy is really popular and could gain TNA a lot of new fans if they keep watching when family guy finishes.