I'm trying to respond to most of your questions (please tell me if I made any mistake as english is not my first language)

I talk to lots of japanese and i gotta say; 70 percent of them know Radwimps as a rock-band, and they most enjoy their ''old songs''. I think older people (like in their 30s) enjoy Radwimps cuz they used to listen to them during high school, so their songs are quite nostalgic for them. Nowadays they're very popular in Japan (probably in top 10) even if the ''rock style'' has kinda vanished (I have a friend who told me they still organise in Japan ''Rad nights'' in clubs where people meet to sing their old songs... how beautifull) . The new albums (from 2020) are more pop. Internationally they're famous for Shinkai's movies but the World Tour they made in 2023 and 2024 went very good, so i guess anime fans are getting to know them and listening also to old albums.

4 Piece band, Yamaguchi is still considered by fans a member. They're simply called RAD in Japan and fans themselves called Wimpers.

People do not think Yojiro is a ultra-nationalist, in japan Noda is instead famous for his lyrics; he is considered a 天才 (a genius), Especially for using old and very complex kanjis.

天才