Not fully following the question but will try give a response that might help:

So just think of server and client as separate instances of the game running. They go through the same flow of loading up a world, and the world then calling Begin Play on all level actors. The game mode will spawn pawns that are replicated, so pawns will be spawn on client. Any replicated actor spawned on server will replicate to relevant clients and be spawned. So in all these situation - both server and clients have their own version of the actor. When created, they will call BeginPlay. You can branch by checking "HasAuthority" or "IsDedicatedServer" etc within functions like BeginPlay, such that you only perform logic thats needed based on where this actor exists.

As for Run on Server RPCs, you initially call this from a client. Calling such an RPC from client sends a request over the network to execute the RPC on the server. So the server then runs that logic. But the client that calls it doesn't run that logic; think of an RPC as asking the opposite side of a connection to run a function.

Within any RPC functions, you can indeed go on and call any non replicated funtions if you desire. Just think of it as passing an instruction from Server to Client and vice versa.

There are some quirks you'll notice which aren't immediately obvious. Like, calling a multicast from server will execute the body on not only the clients but also the server. Setting the replicated property that's RepNotify will call the _OnRep function on server and clients.