I think this is a good forum for airing out how you feel and trying to get other perspectives. It sounds like you are on the right track on focusing on communication. You are within your right to say what you like and dislike. It does not sound like you are being unreasonable.
I think it is good that you see the prroblems being between you and your husband. It would be very easy to blame the girlfriend.
I think in this day and age, parenting/household chores should not be so one sided. However, some people are better at some things than others. When my wife was working, she would come home and cook, and I would do the dishes. I would wash the clothes and she would clean. I think it is fair to look at available time and divide up the chores. But we should allow for preferences.
Your other issue on extrovert vs introvert communication is a problem I have heard of a few times before. I think you have to work on drawing the person out more. Ask questions and wait for an answer. Maybe get them to write down their ideas. Communication is a skill you gain through practice. So try to encourage them to practice. They will still be an introvert, but they can express themselves better when the times comes.