It's true that braces are commonly required for this type of treatment, but that is really because the teeth need to be moved first to the best possible positions for the post-op bite. However, it's possible, if the teeth are essentially already correctly positioned that braces can be skipped - in this case buttons could be bonded to the teeth temporarily for fixation of the splints intra-operatively. Buttons can also be used for orthognathic surgery when lingual braces are being used to treat the case. For patients who do have braces, it is not even true that surgical hooks are always required - depending on the type of brackets being used, it is sometimes possible to attach the surgical splint directly to the brackets without adding surgical hooks.
The biggest thing to understand about these types of treatment is that there is really not a single experience that would exemplify all cases. For one thing, what procedure(s) is/are required varies from one patient to another. For example, in treating an "overbite" (and I am assuming here that what people are really talking about is an overjet

) it may be sufficient to advance the lower jaw (using a procedure referred to as a BSSO - bilateral sagittal split osteotomy), or instead the lower jaw may be advanced and the upper jaw set back (Lefort I osteotomy); yet other patients might, due to suffering from OSA (obstructive sleep apnea), need to have both jaws advanced; or it is even possible (though rare) that the right approach might just be to move the upper jaw back.
Obviously how long the surgery takes will depend on what is being done. But it will also depend a lot on the surgeon. There are some who can get through a bimax case (that is an operation where both the lower and upper jaw are moved) in just a couple of hours or so, whereas others may take longer. This alone will impact recovery time (the longer you're under general anesthesia, the tougher that can be on the body) and will also impact some of the other factors that play into surgery (for example, if the surgery is expected to take 4 or 5 hours or more, a catheter will typically be needed).
Recovery post-op depends on a lot of factors, not least of which being the procedure(s) being performed, and the OMS's skill. But obviously the patient's age and general health can be expected to play into this as well, as can how the OMS manages his patients post-op. As an exmaple, you mentioned weight loss and eating: well, some surgeons will keep all of their patients on a no-chew diet for several weeks, but by contrast, some others mandate a return to soft-chew meals in less than a week. The obvious corrolary to this is that for some patients maintaining weight and ensuring adequate nutrition is more challenging for some patients than for others, and this is bound to impact recovery time.
Eating is also, obviously, impacted by banding post-op, and that's something else that is greatly variable from one surgeon to another, and even from one case to another for the same doctor. Some surgeons generally prefer to keep tight bands for several days, or even weeks, whereas others routinely remove all banding immediately post-op. Similarly, some surgeons will keep the splint in place for a period of weeks, whereas others will routinely remove it from all patients (even bimax cases) before the patient regains consciousness post-op.
Pain is also something that varies greatly from one person to another. At one extreme there will be no pain whatsoever, and at the other there are patients who must rely on prescription pain relief for a more protracted period - not surprisingly, the latter case will tend often to bring with it a slower recovery.
Costs are also incredibly variable. Some "big name" surgeons charge in the realm of $50k for the surgery alone, and that does not include hospital fees; others charge as little as $3k - $5k per jaw, and even negotiate "package deals" with the hospital where they operate, so that uninsured patients can better afford the work if they need it. The cost of the associated orthodontic treatment is also incredibly variable, not least depending on where you're located. One rule of thumb though is that surgical cases are
usually a little more costly than non-surgical.
Six months in braces post-op is certainly a good "average". However, some lucky folks will get their braces removed just a few weeks post-op, and others will still be finishing things up a year or more later. Likewise the amount of time spent in braces pre-op will depend on how much needs to be done.
The question of extractions is an interesting one. Some surgeons will remove wisdom teeth at the same time. But it is sometimes necessary to extract the lower wisdom teeth prior to a BSSO, because the bony incisions are made close to the roots of those teeth. If the OMS wants the wisdom teeth removed ahead of a BSSO, then this will typically need to be done weeks to months in advance to give the bone time to heal and strengthen again before the orthognathic surgery is performed.
The amount of movement that is made to the jaws - and even the precise procedures performed - are carefully considered not only to ensure functional correction, but also a good appearance post-op. The changes can, for some people, be jarring. But usually
most patients will feel that the final results are pleasing. The question about a "jaw implant" is most likely asking about chin implants. This is not commonly done with orthognathic surgery, but a genioplasty - a procedure where the bony tip of the chin is slid forward or back - is not uncommon at the same time as orthognathic surgery, usually to help with the overall aesthetic of the results; when it is done, it is usually considered by insurance providers to be purely cosmetic, and so most patients need to cover the additional cost for that procedure out of pocket. That said, there are studies that indicate that even a genioplasty alone can help with OSA, by the changes it makes to the tongue.
Side effects? Now that's a biggie. Everyone can expect swelling, which typically peaks around the third day post-op; ice packs applied during the first 48 - 72 hours can be very helpful with this. Bruising is also to be expected for all patients. Bimax or upper jaw patients very commonly suffer from sinus congestion for a few weeks post-op. A sore throat is not uncommon (from the breathing tube).
Numbness is also generally to be expected, but for most patients this does generally resolve (albeit sometimes not completely) over time. For BSSO patients, this will usually be in the lower lip and chin, although sometimes it is also in and around the lower teeth and gums. For Lefort I it is common around the upper teeth and gums, and the palate, and sometimes also in the cheeks. As mentioned, it can generally be expected to resolve over time, but for some patients it does not - in this case though the lingering area of numbness is most often limited in extent. Numbness of the tongue is far less common, since this would be due to an injury to the lingual nerve, rather than the inferior alveolar nerve (injury to which is the cause for numbness in the lower lip and chin.
Other side-effects are less common, but might include thrush (an oral infection that can be very painful), infection or loosening of the plates and screws used to fix the bone segments (in which case they are usually extracted surgically), and incomplete union; the latter occurs in about 1% of Lefort I cases - the chance can be minimised by using bone grafts if there will be a large gap - this is something that is going to be more likely in advancements that set-backs or impactions, since that is when a gap is more likely to be created.
Hope this helps create a more general picture.