How do I start dialog / manage gossip in C# with an NPC by name? Or do I have to use LUA?

One more question, how can I check (via either LUA or a bot function) if I can talk to a npc? So basically, I talk to an npc, and after I can no longer speak with that npc, I want to move onto the next step, how would I check if I can no longer speak to an npc using his name?

Hello, you can use c# code: 

wManager.Wow.Helpers.Usefuls.SelectGossipOption(int gossipOption);
wManager.Wow.Helpers.Usefuls.SelectGossipOption(GossipOptionsType gossipOption);

For you second question try this code:

            var unit = wManager.Wow.ObjectManager.ObjectManager.Target;
            if (unit.UnitNPCFlags.HasFlag(wManager.Wow.Enums.UnitNPCFlags.Gossip))
            {
                // ...
            }