Some quick questions

1. Migration is currently a matter of using a script or other tool to invite your new account to all the rooms your old account was in, and then (optionally) parting the old account. It's a bit like migrating between IMAP servers, and generally cumbersome and suboptimal. We're trying to replace it by decentralising user IDs, so that user accounts can span multiple servers, at which point we get migration for free. This is https://github.com/matrix-org/matrix-doc/issues/1228.

2. There isn't a global user directory. Directories are instead done per homeserver, and search all users you share with a room with (or are present in public rooms existent on that server). In practice tends to work relatively well, though, as on a busy homeserver, many of the users you want to find will already be hanging out in public rooms (a bit like on IRC).

3. You have to run a TURN server, but we provide easy instructions for how to do so, and most of the docker or ansible setups automate this: https://github.com/matrix-org/synapse/blob/master/docs/tu.... We don't have the same problems that Jami has due to the thinclient nature. Even when we go fully P2P this shouldn't be a problem, given TURN & ICE is pretty straightforward (mainly due to pre-Matrix us being a VoIP stack shop...)