1. Can I initiate a challange with some characters whose total str are 0? I know that I cannot win if the attacker's str is 0, but can I just initiate it?

2. Can I put into play a shadow character by manning or some effects like that?

1. Yes. There is nothing that prevents you from initiating a challenge with zero strength. Lost Oasis and other effects like it would still be valid effects, plus there are other ways to add strength later.

Thank you!