Use Mozilla's homeserver instead. A far better experience, presumably because it runs on New Vector's modular.im infra. Supports SSO (can even sign in with your Firefox account).
Will that fix things? Apparently, when I tried to DM my friend and invited him to a DM, the room should have been his username but was "empty room" instead.
It may. Riot can be a bit of a pain to get the initial handshake going. If all else fails just keep blowing up the room and retrying until it sticks. I've had to do that before with members of my team.
We're not aware of any performance problems on the matrix.org server right now (we had a breakthrough in performance last week), so I think something else is going wrong. What clients were you using?
hm, weird - not seeing anything around 14:20 on the graphs. might be network connectivity or something else going wrong, but not an overloaded synapse for once.
status.matrix.org exists but is fairly useless - we need to publish the graphs publicly.
P2P is an entirely separate codebase & deployment. The issues here sound like a bug in the legacy Riot/Android app which is about to be replaced by RiotX. In general things have been getting progressively better.