So sorry you have to go through this.
They'll probably give you some heavy duty tylenol - no aspirin products because they don't want you to have bleeding. (You'll be told not to take any of those products for 24-48 hours before surgery too. That's routine.)
Your recovery will vary based on how long the surgeon is in there and how much he/she has to do. More surgery and more manipulation of everything in there causes more inflammation and scar tissue. But they will adjust your meds in the hospital and have you let them know your pain level on a scale of 1-10, and they will want you to tell them how you are doing. They will most likely give you medication through the IV at first, so it will take effect quickly. Exactly what they give you will depend on any allergies you have, but there are a number of choices available that are very effective.
However, since it is laparoscopic, the 2 incisions will be very small and not require a whole lot of healing.
The gas is used to inflate the abdomen so the abdominal wall is lifted and the organs are separated a bit so the surgeon can see how big that cyst is, what it's touching, and how best to remove it. When the laparoscope is removed, most of the gas escapes. However, there's always some residual gas that stays for a few days. It's harmless but you may find you are a little bloated feeling and that your belly is distended. The gas is absorbed and eliminated, or expelled. So you are likely to be more flatulent than usual. For the first few days, eat small meals or snacks several times a day, and don't let yourself get constipated. Avoid gassy foods like beans and broccoli, and anything else that triggers that for you, just for a couple of days. It will make it much easier for you.
The phrenic nerve goes from the abdomen to the shoulder area, so it is very common to have some shoulder pain when you start sitting up. The gas rises, presses on the diaphragm and you feel discomfort. You'll think it's something else because it's such a weird place to get pain after abdominal surgery. It's totally harmless, so don't worry. It's also easy to get rid of. The key to getting rid of this pain almost immediately is to lie down, flat, no pillow. If possible, have your head lower than your abdomen - put a folded blanket or a pillow under your rear end to raise it higher. The pain will go away right away because the gas rises - you'll redirect it into the abdomen. As you are able, try to move around a bit, either getting up for short periods of time, walking, or changing position from side to side. That helps move the gas around, increasing the speed of it being eliminated from your body.
Good luck! I'm sure it's not going to be as bad as what you imagine in your fears. Just line up a lot of help at home so you don't have to do anything - have someone help you get up off the couch, do your meals, and everything else. Let them spoil you. Start up your activities gradually rather than trying to do too much too soon. Your hospital team should be able to give you a better prediction once they know how your surgery went. But overall, laparoscopic surgery is done whenever possible for the very reason that the recovery time is so much faster and easier than invasive abdominal surgery.
Good luck!