There is a real operation to lengthen the leg by cutting the femur and then bracing it with a 1-2cm gap which - hopefully - will fill in with new bone.
It was popular in China as a cosmetic procedure to increase overall height. A few years ago the Chinese government banned the practice, as the complication rate was alarmingly high - a lot of people were ending up in wheelchairs for life.
I don't think that the "bagel-head" was ever actually popular in Japan - that was more of a "Japan WTF" thing that became popular on social media and news articles that love to publish articles about how Japan is a very peculiar place.
However, having snaggle-teeth (protruding canine teeth) - called "yaeba" in Japan - is quite popular amongst Japanese women, as it's thought to make them look cute and youthful. Women will actually pay for a dental procedure to make their canine teeth stick out more.
Speaking of leg-lengthening, a female politician here in Australia went to Russia back in the early 2000s to have the same type of leg-lengthening surgery. Apparently, it increased her height by 8cm and she later wrote a book about the procedure, entitled "God Made Me Small, Surgery Made Me Tall".