Yes, between 1993 and 2018 I lived in Indonesia for a total of 17 years.
While it is technically true that Indonesian (Bahasa Indonesia*) is a second language for many speakers, who use a local language at home and in the immediate community, it is becoming increasingly common for it to be the dominant language among younger folks. Since all official business is conducted in Indonesian, mass media is in Indonesian, schools are taught in Indonesian (and national exams are in Indonesian), candy wrappers and street signs are in Indonesian, and so on, it is more and more the language of choice for everyone all the time.
Don’t tell the Balinese that! The Javanese always say that the Balinese language comes from Javanese, but the Balinese resent that and deny it. (I’m not a linguist so I can’t judge, but AFAIK there is some truth to the claim.)
I don’t know that the Javanese language itself is considered “prestigious.” A better word might be “complicated.” Most people, even Javanese, don’t speak it thoroughly. Technically speaking, it has three levels and your choice of every word is dependent on complex considerations of relative status between the people speaking. (So, if I’m a low-status person talking to a person of much higher status, I’d need to show respect by using High Javanese vocabulary with them but they would use Low Javanese words with me.) But to the extent that people use Javanese in their daily lives, sensitivity to those nuances is disappearing.
A significant body of classical poetry is in High Javanese, and some dhalang (shadow puppet masters) perform in Javanese. But your average person on the street, of Javanese descent or not, won’t be conversant with that material.
Not that I have ever heard of. It would be a PITA as Javanese uses a different script and, as noted above, is a difficult language to learn thoroughly.
One caveat on all of the above: I’m not a linguist, I’m merely speaking from my personal observations/impressions over the years. I don’t speak Javanese at all; the few words I know are musical terms and words that have slipped into Indonesian (stripped of their status level considerations). If a language expert were to take issue with anything I’ve said, I’d defer to their knowledge.
(*) It’s becoming common to refer to the Indonesian language as “Bahasa,” a trend that probably started with outsiders shortening “Bahasa Indonesia” without recognizing that this sounds a bit stupid, since “bahasa” just means “language”: for example, in Indonesian, German and French are, respectively, Bahasa Jerman and Bahasa Perancis. So referring to the Indonesian language as “Bahasa” drives purists (me included) nuts. But, language changes and fuddy-duddy refusal to accept those changes invariably loses. So, “Bahasa” it is.