For random streams. How are you seeding the random stream? What are you using to send the seed from the server to the clients?
For draw calls, what size are your cubes for your map, what size is your map, and what are you using as your cube meshes? Try again and use “stat quick” and “stat slow” to pin down which functions are taking so long.
For Flying movement, the character movement component already has a flying mode that you could use, but it might be easier to make a new movement component. It’s a decent amount of work, but it’ll probably function more like how you want if you do it that way.
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I’ve noticed that non-Character-movement replication is a bit less smooth. More jittery. Things like moving platforms on a Timeline.
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This sounds like something is implemented incorrectly. It sounds like you are moving the platforms on both the server and the client, but still trying to use the network to decide where the objects are. If you want movement handled by the network you should only be moving the thing on the server. If it’s something that can be handled locally then it should only be on the client.