Often, you wake, only to find later that you dind't, it is kinda cool.

Have died in a dream, have fallen asleep in a dream but don't think I've ever dreamt in a dream.

I've experienced it. Although not recently. It is funny because usually in one of hte dreams i am usually aware I am dreaming. When ou becaome aware you are dreaming you get soem control over what you dream, although control is limited.

Yes I have

It happens to me occasionally that I'm dreaming and something impossible happens within the dream (a dead relative still being alive, for example.) That's when I realise that it's a dream. That typically rolls straight into another dream, where I'm telling loads of people about the dream I just had, and how I figured out that it was a dream. Then I wake up and realise none of that was real either.

Sometimes. I have lucid dreams, where I know I am dreaming, and sometime I wake up to find I am still dreaming. This is not a problem. What is a problem is that thy are often set in places that I miss but no longer exist. And with people who no longer exist. Well, at least they do in my dreams.

Yes

Yes. I have fallen asleep in my dreams before and experienced a new dream after that. The initial dream was me just going about my day, but the second dream was of flying. My dreams are lucid enough that I can actually feel the sensation of flight. Much like jumping off a swing. And when I woke from that dream into the inital one, I could hear my alarm. And then my real alarm went off.

Yes-sometimes they are serial dreams too.