We've had the yoga discussion before. I've done yoga and Tai Chi before and I think they're beneficial, however hardcore practicioners of either might tell you that fencing, being a sport that encourages asymmentrical development, will ruin your practice. I look at it the other way, fencing makes you asymmetrical, Tai Chi and Yoga help counter-act it, but I'm not an expert by any means. Tai Chi helped my balance and body awareness quite a bit. I'm still pretty much a klutz, but I fear I would be worse without the previous Yoga and Tai Chi. Yoga definitely helps flexibility as well.
You're right, some Yoga positions look--and in fact are--a bit extreme, however the people you see in videos and books who seem to have been transformed into human pretzels have been at it for years so by no means should, or could a beginner get in those positions. Generally, or so I've heard, it's very difficult to hurt ones self doing Tai Chi, if you force yourself too hard doing Yoga on the other hand, you will be sorry. I heard someone who took Yoga once saying that the teacher tried to force people into positions, THIS ABSOLUTELY SHOULD NOT BE DONE, sorry about the caps, but if you meet someone who advocates this run, the other way, fast--in other words, "do not be alarmed Arthur Dent, be afraid, be very afraid" (THX Doug Adams and the Hitchhiker's Guide). It's possible you could learn from a book and there are a few good books out there, but I would recommend finding a live instructor so there is someone to check your form, especially initially.
BTW as far as I know, Yoga has never had a martial application, although the warrior pose does bear some resemblence to en guarde. Tai Chi once did, although it's done slowly now--speed varies however depending one what you're trying to do--you can feel the power in the moves, especially in the later forms--there are 3 btw. The premise with Tai Chi is that in a situation where force meets force, the strongest person wins, but force with nothing to push against is overbalanced--or as my instructor once said, only Superman can stop a freight train, but any idiot can get out of the way. To some extent it's a bit like sucessful fencing, you can get caught up in opposition, or you can disengage around your opponent's opposition and score.
BTW, and yes I know this is getting long, you generally learn Tai Chi right handed from your instructor, and teach yourself to do it left handed--I once could get halfway through the 2nd form this way, but no longer, I've been lazy
