I've struggled with social anxiety (and still do, occasionally). To directly answer your question:
1) Keeping calm:
-Taking pauses before speaking helps.
-Accepting awkward silences/natural pauses in conversations also helps.
-If you find yourself getting flustered, you can interject with, "That's a great question. I think I need a moment to think about that, actually." or something along those lines.
-Doing something while you're talking with others will allow you shift attention away from yourself when you're feeling anxious. Something as simple as taking a sip from your soda and commenting on how sweet it is or commenting on someone's shoes will divert the attention away from you momentarily so you'll have time to collect your thoughts.
2) Possible conversation topics:
I like employing questions/conversation topics that are a little out of the ordinary. So instead of asking, "What do you do for work?" you could ask more interesting questions like, "What about your job makes you happy/fulfilled?" Or instead of, "What do you do for fun?" you could ask "What's the most exciting thing you've ever done?" Or you could ask, "When was the last time you found yourself extremely happy?" Having a prepared list of these 'more interesting' kinds of questions in your head may help you get to know people on a more intimate level. Rather than getting to know where they work and what they do, you may discover how they feel about things, what their values are, etc.
3) Keeping a conversation going:
This can be tough since you don't want to keep a conversation going that isn't going anywhere. However, when you truly want to know more information about someone or from someone, you should just ask. Even if you're boucing around from topic to topic, people tend to enjoy talking about themselves and don't mind being questioned about things if the listener seems genuinely interested.
If you find that a conversation has lulled or you're discussing something that you don't understand/have nothing to contribute, you could plainly say, "Wow, I don't know anything about that. Tell me what it's like/what it's about." There's nothing wrong with admitting that you don't know something and usually, people are more than happy to explain things to people with open, curious minds.
Hope this helps. Good luck! <3