Yes the mass could cause most of those symptoms. I am not a doctor so I do not know about the breasts an moods but I think it is possible.
I agree with HVAC. Ovarian cysts / masses can cause changes in hormones so, yes, breast sensitivity and mood swings are possible. Is your doctor monitoring it for now since it is not too large? If it does need to be removed, hopefully, you will have a surgeon who can remove just the cyst since you only have one ovary and need to count on it for producing hormones the rest of your life. Speaking from personal experience, surgical menopause is a hellish existence!
The lower back pain could be from the cyst or the anatomical / skeletal changes caused by the severing of uterine ligaments during hysterectomy. I am 9 years post- hysterectomy and have occasional back (and hip) pain.