I need some precisions about the card Scorched Earth ( Non-Army characters do not count their STR during the first challenge initiated each round ).

As the character doesn't count his strenght, does he participate to the challenge?

Is he removed from the challenge as soon as he enters it ?

Is he staying until the resolution, then we say the total STR is 0? (I guess this is the correct anwswer)

Yes, the character is in the challenge but his strength is not applied. However, Stealth, Deadly, etc are still applied. Treat him as a character with 0 STR: he is declared, he participates, he is there when the challenge resolves...