Ava likes Mel! She doesn't always understand Mel, but she likes her. And she really admires Mel's passion for justice and her ability to speak her mind. I think Ava's political views would be quite similar to Mel's if she though for one second that she was allowed to think that way.
Yeah, Barney makes her nervous.
I think Ava probably finds Lee's attention quite flattering! She doesn't know how to respond to it properly, of course, but it makes her blush.