Is it normal dreams using real world sounds?

It's impossible to know for sure what happened with the door-slam.

What is certain is that dream-land doesn't have the same time system as the one we use in the real world. When researchers have woken up dreaming subjects mid-dream and asked them to estimate the time that had elapsed since falling asleep, they significantly over-estimated. In other words, their subjective dream-clock was running much faster than the clock on the wall of the lab.

So, yeah, I'm sure it would be possible to wake up recalling a dream sequence that seemed to last half a minute or so and for that to have actually only taken less than a second.

One possibility of what happened is that the door slammed, and in the fraction of a second between the sound reaching you and you regaining consciousness, you retrospectively created the scenario of your boss firing you and slamming the door. From how you describe it, such an incident wouldn't have taken much longer than a few seconds in the real world, so I should think your brain would be perfectly capable of manufacturing the scenario from the emphatic conclusion running back to the start in a split second.

Basically, your brain heard a sudden noise, had to come up with an explanation for it, anxiety you're feeling about the security of your job popped up and your brain said, "Yeah! We can work with that!" It went on to fabricate a dream where the slammer was your boss, the reason for him slamming the door was that he was pissed off with you, in fact, he was so pissed off that he was firing you, and in order to fire you, he would have obviously had to come to your office.

You remember the incident running forward in time in the normal way because when you consciously remembered it on waking, the rational bit of your brain said, "Hold on! That's ridiculous! It's completely backwards. My boss wouldn't have slammed the door, fired me and then walked up to the door, so it must have actually happened in the reverse of that."

Another possibility is that you heard some sort of sound-cues in your sleep which made you know that your sister-in-law was making her way to the front door, you incorporated these into your dream as your boss walking up to your office door, your anxiety about being fired was woven into the dream, and your s-i-l then closed the door. If she's the sort of person who's always slamming doors, it wouldn't be surprising if you anticipated that, too.

The short answer is yes.

They are a collection of images and sounds that you have encountered, rearranged into random symbolism