Hi Kati - Good Luck tomorrow! I had that same procedure done when I was 17 - way before I had my dd last year (at 30) and I was also worried about some of the things that are bothering you. Definitely talk to your dcotor - they should be able to explain the procedure better - so that you feel comfortable with the decision to have the surgery and what it entails. I had some anger afterwards that I didn't expect - just because I realized that I had been rushed into the surgery and was scared and didn't get to really ask all my questions.
Here's what mine was like - maybe yours is similar or diferent:
I had a 10cm diameter cyst on my right ovary - was in serious pain and had thought it was appendicitis or something. When they realzied what it was I had the surgery that night because the doc was afraid it would rupture.
What the laproscopy does, is not remove the cyst but drain it - so the incisions are small - one was in my belly button - so the camera could be inserted, and the actual needles went into tiny incisions along my pubic line. They gave me general anesthesia. They inflated my stomach with air so that they could see the site better. The cyst actually ruptured while they were handling it, so they just suctioned all the fluid, checked to be sure that it was clear (different types of cysts can have different properties, so they will tell you afterwards what kind you had.) They deflated me (not entirely - I felt very bloated afterwards.) Sewed me up and the next day sent me home with a lot of drugs.
For me, it was very painful, my stomach muscles were hard to use and it was hard to walk for a couple of days, but in about a week I was more or less on my way back to normal. I have had some cysts since but they have ruptured on their own, painfully but without any major problems. I have no fertility problems and have not had to have an ovary removed. From what I understand - the only reason you'd need an ovary removed for a simple fluid filled cyst would be that the cyst itself had twisted and cut off circulation to that ovary - leaving it dead. You most likely do not have this problem, but I'm not sure how they can really tell that.
Good luck! Definitely talk to your doc - feel comfortable about the what-ifs first, and get a surgical report afterwards so you know exactly what they did, it will make you feel better, IMO.