Why is Tianjin accepted for Temüjin? I guessed on the last capital of Mongolian Empire. As I see it, the two things have nothing to do with each other (correct me if I'm wrong).
Speaking of Mongolian music, you should give a listen to the Hu (not to be confused with the Who). They're a Mongolian hard rock band (some call them metal, but they're not) that uses traditional Mongolian and instruments and throat singing and is becoming pretty popular around the world. They had their first US tour last year and it did pretty well. Check it out. Definitely something different. Yuve Yuve Yu.
"Term for the vast grasslands of Asia, which includes much of Mongolia" I would use the term "Eurasia" instead of Asia, because it stretches into Europe too, and just because it's generally referred to as the "Eurasian Steppe." I've seldom heard it called "Asian Steppe."
Cengiz
Chingiz
Czyngis
Djengis
Djingis
Dschingis
Dzjengis
Džingis
Dzsingisz
Dżyngis
Geingeas
Genghis
Gengis
Ghengis
Äœingis
Ginghis
Tšingis
Xhingis
etc... all valid spellings somewhere
No. Just no.
:p