Your two problems are actually very common, I've suffered from them and I'm sure tons of other guys have as well. To solve the first you have to reduce the amount of stress hormones in your body. The stress hormones are what is making you suck at talking around people you don't know. When your at dinner with your family you never have to worry about the conversation going stale right? You don't have to think because your brain is so relaxed conversation is natural and automatic. When you walk into a party full of strangers or are on a hot date you suddenly feel awkward and lose your quick witted demeanor. This is just the body releasing adrenaline. The level of adrenaline release dictates your comfort and relaxation in that situation.
The good thing is you can reduce the amount of stress hormones that are circulating and your reactivity to them. So STOP drinking alcohol, smoking, caffeine, etc..These things directly affect us in a way to encourage stress hormones. Alcohol may temporarily make you feel relaxed but there is a rebound effect! In the long run, i.e. when you are sober, you will become more nervous.
Once you've gotten rid of the bad stuff start consistently doing yoga, meditating, and staying mindful. Implement sleep hygiene and sleep 8 hours a night. You don't have to live like a monk forever. Once your feeling comfortable socially you can relax a bit on your habits.
After all these things you have to implement repeated exposures until the brain down regulates the "fight or flight" response associated with situations it thinks are dangerous or stressful. A long time ago I read an article called "build skills in small steps" and applied it to social skills. Before being on a date with a 10/10 you want to make sure you can talk to an average chick. My social skills sucked so bad that I started making conversation by asking a stranger if he knew what time it was. I talked to the bus driver, cashier, waiter etc. JUST TALK TO EVERYONE. Then, consistently get out of your comfort zone by adding a little difficulty. Sign up for some public speaking. Take a leadership role where you have to lead meetings or organize events. Whatever ya gotta do.
I think if you solve the first problem the second problem will solve itself. This may sound crass, but I found that if you are regularly hooking up with good looking women it's hard to be jealous. Your brain sort of stops feeling jealous because it's already satisfied.