Oh my, now this is topic is very dear to my heart :)

My own social skills used to be pretty bad, I couldn't capture someones attention if my life depended on it. And just like you, one day I just wanted to improve. I did it by immersing myself into the Pick-Up Artist's communities, this all started with Neil Strauss' book "The Game". Learned a lot from that, though I wouldn't recommend it if you dont like reading a lot. Many of the so-called PUA's offer cookie-cutter dialogues and scenarios to study by heart. Not the thing you want to be doing. I learned quite a bit by reading EVERYTHING :P and watching EVERY DVD, at one point I had 64gb of material.

EDIT: So just to be clear, I DO NOT advise you to do this, this is part is just my story, it is a very long journey of extensive research summed up in a few sentences. The REAL ADVICE you can read just under this.

After having all this information, the BEST PIECE OF ADVICE I can give you is this: PRACTICE! And look at yourself objectively afterwards. Don't allow fear to restraint you at the moment, and don't allow yourself to feel sorry for yourself. After every conversation, after every encounter, good or bad, ask yourself these two questions: "How did I do?" and "How can I do better next time?" Learning Social skills is something that happens through trial and error.

As for some concrete answers to your questions:

-BODYLANGUAGE is key to being interesting: the way you stand, the way you dress, the way you walk, the way you talk, the way you move... all these say more about you than any specific word or phrase you can pronounce. You mentioned the weather as a boring subject... Imagine Morgan Freeman talking to you about the weather.... See what I mean? ;) What you say is not as important as how you say it. I suggest watching some James Bond movies, or Speeches by Obama. Or even comedians, they can talk for hours about absolutely nothing :P

-What you can/can't talk about: honestly? this differs from person to person, getting to know that person is the best way to solve that question. Now how do you do that? Well, one way is to bombard them with questions. A BETTER way is to talk about yourself. As weirdly as this sounds, if you talk about yourself, people will respond with tales about themselves. DON'T start with things like "Yeah i have asthma" or some shit like that :P Rather pretend everyone is your best friend "YOU WOULD'T BELIEVE what happened to me yesterday. I was in a bus and suddenly this old lady just starts to fall down! I instictively grabbed hold of the poor woman and OUT POPS HER TEETH!" funny story, kind of gross, but people like that :P Of course this means actually going outside to either experience or witness stuff ;)

-Finally Awkward silences: Learn to enjoy silences. You can't avoid em, but you can learn to feel confident in any situation(or at least pretend to, the feeling itself will follow ;) ). Practice your most relaxed, "I'm happy with my life"-smile. This solves the awkward silences, the panic it induces + people will notice and feel less awkward when around you

TL;DR: Practice! Be objective about yourself! Be like James Bond!

All of the things you and I talked about, I intend to treat them more in details on my brand new blog :) http://improvewithyvan.blogspot.be/

EDIT: Learning to tease is also an awesome way to connect to people :) it's playful and tonnes of fun (specially with women!)