That's some great experience, whatever it was Congrats, sounds very cool.

My idea is, that the first one could have been either a hypnagogic hallucination - HH, which is something like a minidream. Or it could have been a WILD/OBE, if you believe in those. Sounds like you fell asleep right after that, that's why you don't remember. Even experiences like this could be easily forgotten, if we don't wake up from them and write them down. Also, we never really set an intent to remember things like this, so we ar enot conditioned to remember.

Sometimes when we are very relaxed, it may feel like we can't move, or it would be hard to move. But that's just a feeling. If it came to it and you really had to move, perhaps you would have been able to. On the other hand, it could have been SP. But in any case, don't focus on SP. It makes no difference if you feel it or not, but if you wait for it or you focus on it, it will hinder your focus on the right thing, which is to fall asleep while keeping awareness. When you lose track of your body and you try to move, most likely you will move your dream body. Same way, as if it was your real body. Once you do that, you realize you are already in a dream and you are still aware.

The second one, when you realized you are dreaming, was a lucid dream, indeed. A DILD, to be precise. First lucids may end quickly, because we are just not used to this strange state of mind and body. And sometimes from excitement. It will get better.

Keep at it and enjoy