

nginx is a very capable web server by itself, the reverse proxy is just one small part of it.
Without more information I’m just guessing, but they’re probably running the whole thing on-device, the CPU in that phone should have hardware cryptography support (For AES), but even ChaCha is pretty efficient in software on chips like that.
Yep, main reason it’s associated with Google because they bought a company (Jibe Mobile) making one of the main backend service offerings and offered cloud hosting of it, so providers just went with that rather than rolling out their own software.
Also with Apple ignoring it in favour of iMessage, Google was the only one supporting it on handsets. Google client + Google backend = people think it’s Google’s iMessage competitor.