Why is it odd that Yoga would be?
I did some gymnastics as a child also. I never thought about it’s benefits in such terms. I mean I figured it helped me with rolling and such but I didn’t think of it as being that important, I figured martial arts was more relevant.
Nice. Is that stuff judged by proportion of body weight lifted or just by weight alone?
Right, I’ve done some Yoga.
By weight alone, although there are weight classes, and you compete against other people in your weight class. Also, (and I may be wrong–they’ve changed the rules a few times since I competed), I think the rule now may be that if two lifters are tied, the lighter lifter wins.
There’s also something called the Sinclair formula that lets you compare lifters across weight classes (necessary because lighter lifters will always be able to lift more as a percentage of body weight, which is why ants can lift 10 times their weight), but prizes are awarded solely on how much you lift.
There’s a Capoeira class in my neighborhood. I might go for that for some aerobic and proprioceptive work. I love my Jujitsu class but it’s kind of a pain to get to, and I am not that big into the style, not high impact enough. Evil Economist poisoned me with his love of Judo. 
With Capoeira I can study what is likely one of the most practical styles out there in modern society as the most likely adversary I’ll face is the concrete when I trip and fall down. If I knew of a Judo class that was convenient to get to, I might look into that as well.
One set of 8-12 reps every other day will increase your strength. Do a weight that you can lift 8 times and keep that weight until you can lift it 12 times consistently. Then increase the weight so that you can do just eight, etc. This is not for the weight lifters and body builders, but for the average guy seeking to become stronger and more fit. If stamina is what you want, do a lesser weight 20-25 times.
While technically true, and while the various ‘myths’ listed are false in the extreme example, they have a grain of truth - while you can’t ‘sculpt’ with a high degree of control, there are definitely things that ultimately affect how the muscle will appear in different ways - building muscle obviously, targeting different parts of certain muscle groups/areas, “pumping”, and stretching muscle - with the right practice and effort even ligaments can eventually be stretched, and of course losing body fat will change the look of all of the muscles even if you can’t target specific areas. Then there’s plastic surgery, which can target specific areas for fat removal and even for muscle attachment to effect the six pack ab look.
I think most people missed the main point of the OP which was to explain why professionals give the appearance that they are using improper form. This looks like it may address that but I’m not sure:
mwas, it’s odd in that most people don’t think of yoga as exercise or strength training at all. They usually think of it as stretching or meditation.
Evil Economist, yeah, that’s where I got the user-name from. I’ve only seen a couple of other people use it online.
I didn’t suggest martial arts because strength training and muscular control is usually (rightly) an adjunct to learning. You do gain some fitness from doing most martial arts but it’s not the goal of the practice, and you’d have much better gains from doing specific training. For instance, there are a lot of guys in MMA who do Oly lifting for explosive power, regular weight training for absolute strength, and usually some kind of hybrid strength/metabolic training for anaerobic and aerobic endurance. Even in something that’s less concerned with technique over results, they tend to focus on skill work during sparring and training, and do fitness work separately.
That’s partly so that they have a fitness base to support them, so that they can afford to think about fighting instead of how bloody tired they are. Another factor is that practicing movements when fatigued has a negative impact on both technique and power; there’s neuromuscular carry-over that can affect their fighting. So instead of practicing punches until they’re so tired that they hit like little girls, it’s better to do a movement that is similar enough to train the right muscles, but not so similar as to impact hard-earned skill.
Oh, and since I didn’t address the OP in my first response, I guess I should probably do that now. IMO, there is one good reason to do partial or “cheat” reps: training through a sticking point.
Other than that, it’s usually a bad idea. The high-level bodybuilders you see doing that are probably experienced enough to know what they’re doing, and they have made the choice to accept the possible negative consequences of training that way. They’re willing to court injury by loading to the point where they cannot do the exercise with good form. They’re willing to sacrifice training optimal movement, and strength over a full range of motion in order to add muscle mass. They’re willing to risk overtraining problems, that they hope to avoid by much more careful management of their training schedule than the average lifter. They’re willing to accept a possible reduction in flexibility in order to look bigger.
That’s the real catch, is that bodybuilding is all about appearance. They don’t care about function anywhere near as much as looks, so they do some training that is not optimal from a functional and safety point of view in order to make gains in muscle mass. These are all trade-offs and anyone training at that level has to know that.
Something else to keep in mind when you view the training routines of some of these guys is that their routine probably won’t work anywhere as well for you. They’ve been progressing for years, and have tailored things to fit the way their body works. In most cases, the volume and loads top builders use would absolutely not work for anyone with less of a training base, even in the unlikely event that the builder in question isn’t doing steroids.
Lots of people who don’t know any better go out and do a chest workout that consists of something like bench press, decline press, incline press, and dumbbell flys, not realizing that the bodybuilder they’re trying to emulate does that amount of volume because he needs to in order to see progress at his level of training. Beginning and intermediate lifters would be far better served by training with vastly lower volume and instead focus on intensity i.e. weight. Even some advanced lifters could probably benefit more from low-volume training than the multiple sets and exercises model of mainstream high-volume work.
There’s an article at the well respected Exrx site covering this in brief.
On the other hand, what you’re seeing might be nothing more than a “pump” routine to get an idea of what he’ll look like on stage, and I could have just wasted countless electrons explaining practical shit for no good reason.
Often, it is mostly stretching and meditation. Anusara (what I do) and Ashtanga yoga are intense strength-building and weight-bearing work-outs, but most yoga classes available at gyms, colleges and even lots of studios are ‘yoga lite’ that require very little effort at all and focus more on the relaxation and stretching aspects.
I hated yoga for years (can’t take new agey spiritualist BS and I would rather practice my breathing exercises in the privacy of my own home) before I found my ass-kicking Anusara instructor. 
No. The reason is that (generally speaking) the bigger the weight, the bigger the muscle. Strict form will limit the amount weight you can lift through the entire motion.
If you are looking to increase overall muscle mass I suggest the opposite. I’ve trained guys who had been training for years and had hit a plateau. By cutting them back to ‘The Big 3 +’ (power cleans, squats and bench presses + curls) for 6 weeks most were able to pack on a good bit of size during that time. That said, when cheating you must cheat with an eye towards the muscle you are trying to train rather than just lifting big weights.
As noted most pro bodybuilders rarely use strict form to build mass. Incidentally, most bodybuilders don’t like to be photographed during the mass building phase so the pictorials routines you see in the muscle mags are usually ‘finishing’ routines as they head into a contest.