I felt partially lucid as if observing the whole scene and my other I worked through the whole experience.

There was only a blackboard visible with one word. In the background i felt a presence of a young woman and a man. There was a feeling of unresolved conflict in relationship from that woman to that man. Then i just erased one syllable from the word and the meaning of the word changed to something that clicked for that woman. She started to cry from understanding this. Also i felt some sort of relief from her, like something old leaving behind.

After waking up my feet burned hot for a while. Then i got it that this was about retrieving someone by helping them understand something important to them.

What was new to me : The feelings after waking up were much more clear and the images/sounds/names/words that were there just vanished like they were not that much important for me to remember.

Sounds like an important experience.  You definitely were helping this young woman through something powerful and emotional.  I wonder why your felt felt burning hot.

Sometimes more meaning comes later.  You might want to try to meditate on it or set intention before bed to get more of what it was about if you feel so inclined.  I always try to do this, but it doesn't always give me results. 

I'd like to hear if you understand more later as time goes on. 

I learned the hard way that it is better to let go. To many unresolved mysteries and questions make the head spin and hurt.  ;)

The hot feets (or other places in body) i think are energy related.