Katniss would likely become more protective. Her natural instinct to survive would be amplified by the need to protect her unborn child. This could make her more cautious in her actions in the arena, but also more fierce when directly threatened.
She might get angry. Katniss has a fiery side, and seeing Peeta with another girl could trigger that. She could give Peeta the cold shoulder and refuse to talk to him.
Katniss copes in multiple ways. She has to be strong for herself, Peeta, and the unborn child. Emotionally, she might bottle up some of her feelings at first, but as time goes on, she realizes she needs to let them out. She could start writing in a journal about her experiences, fears, and hopes. Physically, she takes care of herself as best as she can in the difficult situation, eating whatever nutritious food she can find and getting enough rest when possible. Socially, she tries to keep a small circle of people around her who can support her, and she also tries to slowly re - introduce Peeta to those who care about him in a way that won't trigger his hijacked state.
Their relationship would likely become more intense. With a baby on the way, they'd have to rely on each other more. Gale might become more protective of Katniss, and Katniss would have to trust Gale in new ways.
Katniss might be initially shocked. Given her own tough exterior, she may quickly try to restrain Peeta without overreacting. She could be more concerned about what's causing his flashback rather than her own injury at first.
She might struggle at first. Katniss has always been a fighter, and motherhood is a whole new territory for her. She would likely be very worried about not being a good enough mother. However, with the support of Peeta and her friends, she would gradually learn to balance her new role. She would also use her strong will and determination to provide the best for her child, making sure they have a better life than she did growing up in District 12.
He wasn't sure. The information I know about the source and background of the Ao Ao awaiting arrest comic is very limited. It could be adapted from a novel or an original. If you can provide more information about the manga, I will try my best to answer your questions.