Invidia, the story of the development of the Cherokee syllabary is quite fascinating. Supposedly it started with the equivalent of a bar bet - one of Sequoyah's friends insisted that writing was "white man's medicine" (with medicine in this sense meaning something more like magic). Sequoyah agreed that literacy was powerful medicine, but he believed that anybody could do it. He worked on it for years and years, including while he lived in Titsohili (modern-day Fort Payne, Alabama, where I grew up not three miles from where the great man had lived). Some of the more superstitious thought he was doing witchcraft (defined as using medicine for evil purposes), including his own wife. But he persisted, and finally developed a unique syllabary with flowing, curly characters.
After finally getting buy-in from both eastern and western Cherokee leadership, he went to a print shop to see about getting a set of movable type created. The price quote was eye-watering. So he took stock of what characters were available in the movable type at the print shop, and re-worked the syllabary so that existing type could be used (sometimes with slight and inexpensive modifications).
The result is the modern Cherokee syllabary, which includes characters from the Latin, Cyrillic, and Greek alphabets, plus some characters that I haven't yet identified.
> Are older relatives the predominant means of Cherokee learning their native language?
> Or are there education programs etc.?
The government used to have a policy of actively suppressing native languages ("kill the Indian and save the man"). Thankfully the government has reversed that policy! For many years, it was the elders who taught it. But many did not want to teach it - thinking that it would be better for the young people to just speak English. A sizable minority stubbornly held on to it, though, and taught it to the youth.
These days, though, there are indeed education programs. It's taught in schools in parts of Oklahoma and North Carolina. The Cherokee Nation (the largest of several tribal entities) offers classes for adults who want to learn. Other tribes have similar programs (such as the Chickasaw Nation in Oklahoma), often funded by casino proceeds. (I will not comment on the morality of gambling as I am personally ambivalent to the practice, but the casino revenue has been a real life-saver for many tribes.)
As for myself, as a mixed-blood, I straddle two worlds: the white and the red. Sometimes I feel as if I have two men inside me: a white man and a red man. I try to take the best of both worlds as much as I can, and this includes the music. Sometimes I wear a European hat, so to speak, and geek out over Bach, Beethoven, Chopin, etc. And sometimes I wear a Native hat (sometimes literally; Cherokee headdresses are more like turbans and not the feathered warbonnets that most people think of) and play my drum and sing of the old gods and spirits.
I'm actually lucky compared to most of Indians. I received a good education, got a PhD, have a decent day job, have a concert grand piano, have some excellent piano students who respect me and actually practice... Most of us aren't that lucky, even for Cherokees, and we're some of the wealthier Indians. (Consider the Pine Ridge Lakota Sioux...)
Oh, well... probably more than anybody cares to read. But language (and by extension culture) is a complex topic. It's made even more complex at my house because the rest of my family is Taiwanese, which introduces even more linguistic issues...