Yes, it's still the same memory as everything else. It's more like a book or description.

It's still not the norm. I have normal dreams without being wake in them or waking up from them. According to my "research" (asking friends and family) I dream a little bit less often than other people - maybe one dream per week or two.

Yeah, I can also wake myself from those dreams by raising my heartrate and it won't be throbbing when I actually wake up.