Yes and no. Without self-awareness, those thoughts are just instinctual desires, e.g. 'need food'. Without self-awareness there won't be much going on in any dreams either.
Not only feasible but equally valuable. It’s simply how humans orient their thoughts, and we have no evidence that this has intrinsic value over a being which doesn’t do this.
You're making an awful lot of assumptions that contradict our scientific understanding of animals. A being without self-awareness would only have thoughts that are basically instinct, i.e. 'need food', and those thoughts are in no way equally valuable to more complex thoughts.
I’m not positive that’s true though. There’s so much we think about the world that seems to only be an extension of how we experience the world, but can’t be verified at all. Such as the idea that without an “I” as we experience it, there is no meaningful awareness. I’m open to animals having experiences which are different from mine yet still worth something, and generally worth preserving in the way we typically believe we should with, say, a cat or a dog.
Memory can be separate from self-awareness, and that's the thing we need to try and be aware of.