After giving birth, will I be moodier during my periods?

Unknown. Everybody is different. Usually periods are less painful and easier but everyone is different. You will have to wait and find out how your moods vary with your periods until after the baby comes to find out.
It depends. If you were never moody with your periods before childbirth, there's no reason to expect a change. I don't think childbirth affects PMS at all, but having a small baby might well lead to more stress, and less sleep, which can both cause mood changes. Periods themselves, and cramps, can change after childbirth. Often cramps resolve, and heavy periods become lighter.