A: The way DRRR does online is fundamentally incompatible with Emscripten. Because of how web apps work (sandboxing), they simply don't allow data to be sent straight to random IPs over UDP.
A: Hit clear all data, refresh, then hit start. This will erase your saves, but you shouldn't have any if the game won't start.
A: No.
A: Mainly browser overhead + a lack of thread usage. Not much I can do here, sorry.
A: That's not a question. Anyway, enable fullscreen in the game options.
A: Feel free to DM me on Discord (yuriko.shimizu) and I'll have a look.