She's only human, of course she gets emotional. And Leela have always been an emotional character.
In "Bend Her" Bender was making a mockery out of her gender, so it's a bit understandable she's irritated with him. As are Amy.
"The Sting" was mostly a dream, a dream where Leela thought she were losing her mind. Those weird things would make everybody nerveous. The first part showed her controling her fear and emotions, just to prove they were a skilled crew.
TMLH. If I got the chance to relive a lost youth, I'd probably be just as excited. Though I wouldn't insisit on a cerfew [?], or say no to beer/tequila.
In "The Why Of Fry" she was just happy to see a good friend do something nice to her, after a rotten date with a heartless sleazeball.
"Less Than Hero", okay that one I can see. I'd expect Leela to come up with some kind of rescue plan instead. Although as obnoxious her parents were portrayed in that ep, I see why she didn't feel like taking risks.
What I'm saying is: she reacted emotional in all of them, but I don't see this as a new development, or signs of a stronger emotional drive, since it has always been part of her character. If anything I see what I mentioned above.
Just my .02 kroner.