It's hard to answer the pain question as everyones tolerance to pain is so different. I'm never really bothered by waxing, I don't generally find it painful, even XXX waxing, but others are in agony!
Some people recommend taking anti inflammatories like nurofen etc an hour or so beforehand to take some of the edge off, but it's up to you.
The redness/swelling will def be gone in a week. I would probably get it done even closer to the wedding. You will probably need to stop shaving 2-3 weeks prior depending on how quickly your hair grows