Context

In the game I'm working on (a sort of a point and click graphic adventure), pretty much everything that happens in the game world is controlled by an action manager that is structured a bit like:

So for instance if the result of examining an object should make the character say hello, walk a bit and then sit down, I simply spawn the following code:

var actionGroup = actionManager.CreateGroup();
actionGroup.Add(new TalkAction("Guybrush", "Hello there!");
actionGroup.Add(new WalkAction("Guybrush", new Vector2(300, 300));
actionGroup.Add(new SetAnimationAction("Guybrush", "Sit"));

This creates a new action group (an entire line in the image above) and adds it to the manager. All of the groups are executed in parallel, but actions within each group are chained together so that the second one only starts after the first one finishes. When the last action in a group finishes, the group is destroyed.

Problem

Now I need to replicate this information across a network, so that in a multiplayer session, all players see the same thing. Serializing the individual actions is not the problem. But I'm an absolute beginner when it comes to networking and I have a few questions. I think for the sake of simplicity in this discussion we can abstract the action manager component to being simply:

var actionManager = new List<List<string>>();

How should I proceed to keep the contents of the above data structure syncronized between all players?

Besides the core question, I'm also having a few other concerns related to it (i.e. all possible implications of the same problem above):

• If I use a server/client architecture (with one of the players acting as both a server and a client), and one of the clients has spawned a group of actions, should he add them directly to the manager, or only send a request to the server, which in turn will order every client to add that group?
• What about packet losses and the like? The game is deterministic, but I'm thinking that any discrepancy in the sequence of actions executed in a client could lead to inconsistent states of the world. How do I safeguard against that sort of problem?
• What if I add too many actions at once, won't that cause problems for the connection? Any way to alleviate that?