Hi Ikarus,
I am about to (actually in 2h time) remove my third one, having removed 2 last week. The process is not painful at all and the recovery takes about 1 week ish. That is the hard bit. During that time (or the first 3-4 days really) your cheeks will be twice their size, it will be hard for you to eat and it will be painful at times (very painful if you don't take your prescription drugs, so don't be a fool like me and buy them straight away or you will regret it, especially for the first day).
Apart from that, nothing major. One of my teeth was very very close to a nerve, so I was at a higher risk of suffering from paresthesia after the removal (which is a tingling sensation in your mouth which can actually be chronical). That is the only thing that can be a bit worrying, but not really. My doctors said that even if it happened to me nobody else would notice it and it would not affect my speech so my RT would be safe!
Before removing them I had no issues at all with them whatsoever, so I can't really tell how much you are going to improve with the operation. I just removed them because 3 of them were found to be in a dangerous position years ago for another X-ray checking my gums.
Finally, I have heard that you can't really fly in 2-3 weeks time (can't tell you because I have got some weeks off now and won't be nowhere near that), but that is something that you will have to work out once you have your appointment with the doctor. It took for me some time to get things done before the actual removal so if they are bothering you get your phone and call them asap
