Does all deductive knowledge stem from inductive observation?
Strictly speaking, there is no "deductive knowledge" and there is no "inductive observation". There is only knowledge, observations, and beliefs. However, what most people would call knowledge is actually beliefs. They would say they know they have a tree in their garden when in fact they only believe that. This is also why our theories are revisable. If we knew our theories true, we could never revise them without producing a false theories instead.
Deductive logic is all we need in a world about which we know nothing, not even that there is one. We only need deductive logic because we are capable of living our lives on the sole basis of our beliefs about the world. We trust our senses. People who don't starve to death and don't reproduce and their genes are selected out. People may be dogmatic about things like God and what not, but they are all prepared to revise some of their beliefs whenever their senses make them feel the pain of their mistakes.
To express this in your quirky terminology, inductive knowledge follows from inductive observations, and this is all we need to survive in our world.
What about knowledge itself? Well, clearly, there are things we know. I know I have the impression of seeing a tree in my garden. From this, I will derive the belief that there is a tree in my garden.
So, essentially, we know what we know, and logic never gets to be used to infer any knowledge which is not already apparent in the premise. So, if the premise is that I know I have the impression of seeing a tree in my garden, then all I can infer is that I have the impression of seeing a tree in my garden.