Should I make the first move?

There is a girl I have known for a while because she lives in my locality, and we have some common friends. Whenever we meet at a party or gathering, I get the feeling that she is flirting with me. I am definitely interested, but I never say anything directly because I don’t know if she is serious or not. If this is her nature and she is just a friendly person in general, I worry that my misunderstanding will cause a lot of unnecessary issues and create an awkwardness that isn’t there. I don’t want to embarrass myself, but I also don’t want to come across as clueless if she is waiting for me to make the first move. What should I do? Should I ask her on a date and see what happens?
You can always ask her out for coffee and try getting to know her better without assuming there are romantic feelings involved. Awkwardness about any possible misunderstandings can be avoided by having conversations in a neutral setting. It’s possible that she is just friendly at parties, so a one-on-one chat can give you a chance to gauge her intentions, if they exist. It’s always best to chat as much as possible because, as two adults, the ability to be direct can only be possible when you have established a level of comfort with each other. If she isn’t interested in coffee, you will have your answer.

I had a party a few days ago and ended up getting pretty intimate with a girl who happens to be a friend’s girlfriend. I don’t know if I should tell him this because it will destroy our friendship. Should I say nothing and hope he never finds out?
That depends upon the importance of openness in this friendship, your hope that his girlfriend doesn’t mention it, and what you would like to happen if the situation were different and this was your partner involved. Honesty is always critical for the longevity and strength of any relationship.