Besides...How could Aizen TELL Ichigo was human?
Because he's Aizen and he knows shit?
Is a shinigami a human? If you were to sample the blood of a shinigami would it be genetically human?
Yes. Shinigami are a species. That's made explicitly clear.
Does that mean our soul is made of flesh and blood seperate from our body?
Yes. Again, this was all explained eons ago. Apparently, tons of people have forgotten about it.
Shinigami, Hollows, Pluses, and all other spiritual beings have bodies that are made of "reishi," or "spirit particles." However, living beings are made of atoms.
To summarize it incredibly short: Reishi isn't just some throwaway thingy that the Shinigami use, like ki or chakra or whatever. Reishi is a fundamental particle.
To give you some perspective to what that means, there is currently only one known fundamental particle in existence IRL. The atom.
However, in the Bleachverse, there is a
second fundamental particle that exists alongside atoms. It is the spirit particle.
So yes. Souls in the Bleachverse have flesh and blood and bone separate from the 'atom' flesh and blood and bone. That's why Shinigami can get broken limbs, and why Hollows bleed. They all have brains, and hearts, and livers, and stomachs, and blood, and bones, and muscles. They just aren't made of
atoms.