Yes have done this. I'd say I go very in depth because usually I only remember a little bit anyways, so I just talk about everything I remember/wrote down.

I thought all dreams were strange? All of my dreams are strange and I usually want to discuss the strangest ones. I'm not sure what you mean by bad dreams, i.e. embarrassing ones or scary ones but I've talked about both. In my mind you should never be embarrassed by a dream. I mean I know I have been, but it really is kind of silly.

You should be able to talk to your therapist about anything.