Have a cyst on my left ovary that is 6 cm, will I need laparotomy?

Probably not. Laparotomy involves opening the abdomen with a large incision. Many ovarian cysts can be removed laparoscopically through small (<1inch) incisions. The advantages are less pain and shorter recovery time, in addition to smaller scars. This being said, some cysts may have to be removed by laparotomy if there is scarring in the pelvis.
Depends. It depends on the skill of your surgeon and the concern over the possibility of cancer which relates to your age etc. In our hands, in young patients with "big" cysts up to say 12 cm or so, we would almost always approach with laparoscopy unless a malignancy is strongly suspected. This would be rare in the young age groups. Depends on the planned surgery and the indication.