I would guess that it means premier as in, the highest in quality or degree, since it suggests that a chess club in Paris might be particularly luxurious or exclusive. I think if it were referring to the age of the club, it would say 'oldest'. Also, so far as I know, Paris didn't have the first chess club in the world, but I could be wrong about that. I'd assume the first club would be somewhere in India, nearer to where the game was invented.

The first one is "I'm standing here judging you, you big fucking bellend." Which is an insult not unlike 'dickhead'. And he's talking about eating a Terry's Chocolate Orange in the part after “But as far as you’re aware I did have a bowl of fruit, so I should be commended.” I'll try to transcribe that part, but it might take me a minute! As a disclaimer, I've only lived in the UK for about a year, so I am by no means an expert. I am a fan of this comedian though, and he's often on game show programs, so I have had a bit of practice listening to him.

It's an idiom that means completely unable to hear. In that phrase, post means something like a piece of wood stuck in the ground, as in sign post. Naturally, a post cannot hear, so the phrase: "dumb as a post" means unable to hear. "Blind as a bat" is a similar idiom, except it means unable to see.

That's not a phrase that I've run across very often, and it sound a bit old fashioned to me. A barb is like a sharp point or thorn, so it can also, figuratively mean a cutting insult: https://en.wiktionary.org/wiki/barb#English (meanings #1 and #2) So I'd say for example that someone had a "barbed wit" if they were often saying cutting or mean remarks in a smart or funny way. So I'd maybe interpret that as meaning: that person says insulting things that have a stinging effect.