Hi @Kalimero,
Thank you for the kind words, we'd love to have your students use Mattermost for communicating,
Regarding mobile notifications, they currently function based on email notifications (only sent when you miss a message while disconnected), and in Mattermost 3.1, releasing June 16, there should be an option to make them work more like desktop notifications, which message you even when you're online.
Functionality of push notifications shouldn't be affected by connection speed, it's probably more expectations of how they should work (which has already been addressed in code, you just need to wait until the next release).
Regarding HTML rendering and performance, we have benchmarks published on response times for iOS and Android apps on networks 4G and higher and performance seems competitive to full native apps.
Would these benchmarks be acceptable for your uses?
Because EDGE and 3G networks are declining around the world, it hasn't been a top priority to support those standards.
That said, performance is an area we want to constantly improve and contributions to increase performance on slow connections would be highly welcome.