how many times do I have to do the training mini game with Mikasa in order to be more 'bold' with her? Also after doing squats with Sasha, whenever I go to the barn with her MC says he doesn't have anything to say to her.
Finish training with Sasha, then go to the barn with her. And currently, training with Mikasa doesn't progress the story, you meet her in the evening on the training grounds and take her to "special" training. Fighting training will be needed next update.