Much as I like your translation notes, this time you fell for propaganda.
- Karate is not Te, and vice versa. Karate is a castrated version of it that was developed as a less dangerous sport for japanese primary schools by Funakoshi. Te and karate are kinda like Kalapuriyat and Yoga - one's a martial art, the other is a sport for kids and grannies that happens to have some movements in common. And yes, there's also schools of "Self-Defense Yoga", which are about as usable as Shotokan Karate.
- Mixed martial arts don't use "whatever works". They accept fighters from any school or style, but also enforce rules that are just as strict (or even stricter) than in traditional arts. Usually, the rules are meant to force fighters into grappling matches to make the fights last longer (and thus give more space for advertising).
Promotions banning fighters, or in some cases, entire organisations, for being "too effective" also happens regularly.
To paraphrase the UFC (from when they refused the Dog Brothers participation in an open letter): It's not about realistic fights, but about giving the viewers what they want to see.
- Ju-Jutsu and Jiu-Jitsu are completely different systems. Ju-Jutsu is German, and was developed in the last century. It's an early MMA, and absolutely ridiculous (among other things, you're not allowed to defend against throws). What you're describing is Jiu-Jitsu.