To 1 and 2 I can't answer because don't know exactly what's hapening. Seeing the screenshot you posted I assume you are "cloning" the Ghost Shooter multiplayer example that comes with Construct.
If so, the only thing I could advice to you is to check the Sync statements on the Signalling section and look if all variables controlling ship movement are synched. And if so, perhaps change his mode of "Interpolation" to see if that resolves the placement problems you are experiencing.
In the multiplayer games I'm developing I'm using a mechanism to synchronize some Arrays with data about each player between all peers and host (cards each one has in hand, cards played, ...). But position of sprites is left to the Multiplayer plugin and his synchronization mechanism.
About point 3, in the games I'm developing I put a screen in the "host" that shows "peers" as they are being connected. And a button to "Start game!" when the host sees all the "peers" are already connected. The host is not a player, is something like a "game-master", controlling the other players, maintaing synchronized all the underlying data, ... He has controlls to modify the state of the game and also to "kill" the game if he decides to do so.
Also, on top of this, there is a mechanism implemented to control the reconnection of a "peer" in case it disconnects in the middle of a game, saving his state in case of disconnection and restoring it whenever the peer connects again. Only connections of peers previously connected are allowed. We check it using the "nickname" introduced on first connection. Not the most efficient mechanism but it works for our needs.
Don't know if I have given you the directions you need to implement point 3. It's tricky because the Multiplayer model of Construct, but doable.