Yes, enemy attacking during your turn is an issue I'm looking into, alongside some other bugs, including the chicken game malfunctioning. One thing is that you don't actually have to finish the chicken game, you can just lie to the Eggcellency and go on, in case you're stuck.
As for angels, they do have a lot of red attacks, so when you start getting power ups, it becomes easier to counter them. The game revolves around obtaining all the necessary tools to stop angels from being a threat