are these lucids?

So twice now, I've had these lucid dreams within dreams.

One of them was pretty vivid. I remember dream-going to sleep, and then waking up and becoming lucid. I was fighting spiders and jumping around, but I woke up in my lucid dream, and returned back to my dream.

For my other one, I remember falling asleep in my dream and the lucid dream in my dream seemed really hazy. Right when I realized I was dreaming everything started to fall apart and cracks formed, and I woke up in my dream. A little later I woke up in real life.

I don't really think these are lucids. I wasn't really conscious of them, but I think my dreamself was. I don't know.

Sounds like you woke from your LDs into false awakenings. Try doing a reality check every time you wake up, this way you'll realize your in a dream if you have a FA.

By the way, lucid dreams can range greatly in for lack of a better word, awesomeness, some lasting only a minute or so. If you gained awareness then you are lucid, even if it is lost over time or shortlived