I've had an emergency and an elective section. Both were very calm and basically the same process, but I did recover much faster from the elective one. That's possibly because I'd done it before so knew what to expect, but it was less painful afterwards anyway.
Both times I got to hold my DC as soon as they were born and could breastfeed them as soon as I was wheeled into recovery half an hour or so later. I probably could have BF them in theatre if I'd asked actually, I'm sure they would have facilitated it. I won't lie, the day after was pretty painful (tbh the first 4-5 days were pretty bad after the emergency one, but I was very ill anyway hence needing a section). With my elective section I was honestly not in much pain at all after a day or two.
In terms of the actual surgery, the bit where the spinal anaesthetic is put in is the only bit I was scared about. I needn't have been, it was just a very odd sensation! Like when your face is numb at the dentist, but from the chest down. I could feel a lot of pulling and tugging going on but I couldn't 'feel' it in any painful way, just the pressure of being pulled around I suppose. A bit like someone doing the washing up in your tummy, as my midwife put it.
It didn't affect my milk coming in at all, my eldest son was in scbu after but that wasn't related to how he was born, and I was driving after 4 and 3 weeks. My scar (scars? The second was done in the same spot so only one scar apart from an inch where it deviates) healed well and was a thin silver line within 12m. That's impressive given how red and angry it looked at first. I worried as I had a big numb bit around the incision, but that returned to normal over a few months. I have friends who found it harder than I did but also friends who now have huge, lifelong issues due to having vaginal births. I'm now glad I had sections tbh.
And no, your bits won't be affected in any way at all as they're not doing anything to your bits! This is supposed to be one of the benefits of having a section but I've not done it the usual way so can't comment. You'll have a catheter put in when you're already numb, so it doesn't hurt at all. That's just until you can get up and get to the loo, which will be anything from a few hours later to next morning depending when you have the surgery.
Can't think if anything else but if you think of any more questions am happy to answer.