Thanks! Reinstalled and deleted save data like you told me and now it seems to work fine. I'm looking forward to play story mode :)
However, after I pressed the "delete all data" button, I couldn't interact with the game - seems similar to other two bugs. I couldn't tell if it did something or not, and couldn't go back either, so I had to quit the game from OS. Not a major problem, I opened the game again after that, and everything worked, I could create new save/character etc.