Alright, so it seems like the heart of your question here is how to resolve the dwarf NPC picking a verbal fight with your character. It’s difficult for me to figure out how exactly I would execute this, because I don’t know the context of why this fight is happening in the first place - did you insult the dwarf somehow? Is this an encounter I’ve specifically set up as DM? I don’t know, there’s different ways I might handle this. But ok, let’s assume this is part of a planned encounter - maybe the dwarf is part of a local gang you’ve been causing trouble for. I would describe the dwarf’s action in terms of goal and approach. So, the dwarf wants to… What, get you to leave the tavern? Sure, let’s go with that. I’d tell you that the dwarf makes it clear that he and his friends want you to leave, and you can do it the easy way or the hard way. He puts his hand on the axe at his belt as he does so - not drawing it yet, but ready for if a fight starts. His companions follow suit. What do you do?
That’s a reasonable example of how an interaction like this might go down at my table. Note that I’m just following the basic pattern of play, describing the environment and then letting you describe what your character does in response.