Do you remember many of your dreams, or only occasional ones?
I remember them when I wake up, but these days I don't usually write them down, and I forget them within half an hour or so.
Of the ones you remember, are they typically happy, or not so happy?
To me, "happy" implies a fairly simple, one-note emotion. My dreams are almost never "happy." Sometimes/often I feel a lot of joy or awe or excitement some other positive emotion. But in the past month or so I've had very dark dreams. I'm not sure why. I thought it was because I was going to have surgery, but now that's done with and I'm still having them.
Do your dreams have any recurring themes or characters?
Recurring themes: equipment that I can't get to work properly (phones, ATMs), large byzantine structures (airports, parking garages), places where people meet temporarily (camps, conventions, hotels), sinster secret plots, being ignored, having social anxiety, meeting someone exciting
Recurring characters: the (Jungian) animus
Do your dreams give you any insight into how you feel or why you behave the way you do, or do you think that they're just stories your brain creates to pass the time?
Something in between. My dreams give me some insight, and I can usually trace some of the elements in my dreams to stuff that's going on in my life. But I don't think they're deliberately trying to send me messages. When I analyze them, it's more like how I approach analyzing a spread of tarot cards: the insight comes from how I approach the content and what my approach says about what's on my subconscious mind, as opposed to a supernatural influence.