1. The only evidence for physicalism is that doing things to the brain affects the mind. This is expected by everyone though, dualists for instance don't say the two aren't connected, it isn't exclusive to physicalism. It also forgets that correlation isn't causation. And the conclusion doesn't even follow, for instance if I break my TV and can't watch the news anymore, my TV still doesn't create the news.
If your leg gets broken, nothing was done to the brain directly but the mind (and brain) are still impacted alike. We can find no division or distinction between the two. When higher brain functions cease there is no consciousness or mind. If the two are separate then what happens to the mind whem braindeath occurs?
2. We cannot rely on a faith that one day science will show the brain creates the mind.
Except that's where the evidence is pointing. In fact it's already there. Such as, we know things like childhood abuse and operationt conditioning do effect the brain, and these effects, such as a malformed prefrontal cortex manifesting as symptoms we can see in how the "mind" takes in the world nd processes it
3. Matter and minds have mutually exclusive properties and so cannot be reduced to each other.
What mutually exclusive properties?
4. Matter is only known through mind so we cannot reduce mind to matter.
No, we can test and measure matter. There's no valid or good reason to accept solipsism as real or credible. The matter of the Cosmos was here long before any neurons existed that could take it in and ponder it.
5. The existence of consciousness is undoubtable but matter's existence can be doubted, so the first cannot reduce to the second.
Except consciousness can be doubted, with many claiminy it's nothing more than an illusion.
6. Consciousness also affects the body the same way the body affects consciousness.
That's just not true if we fully think this one out. Like birth defects. Thats happen regardless of the mind.
We also call it denial when someone maintains hope in face of certain doom, such as refusing to accept a terminal diagnosis that goes on to kill regardless what the mind thought of it.
7. If we were deterministic mechanical processes we could not have the free will we possess.
Free will has never been shown to exist, amd things like upbringing amd genetic predispositions make the belief in it just as absurd as fairies and astrology.
8. Evolution doesn't explain how something with properties mutually exclusive to matter can exist.
What mutually exclusive properties? It seems more like you're trying to take some pages fron the Young Earth Creationist playbook by trying to create confusion where none exist.
9. Emergence doesn't explain the relationship between mind and matter because emergent things share properties of what they emerged from. For instance you can both see legs and "running," feel a leg and feel the air as they run by you.
That doesn't mean we have some voodoo hocus pocus aether stuff going on. It just means we have an imagination that lets us envision things outside of our own perspective.
10. Physicalism does not account for the existence of logical or mathematical laws as they are immaterial.
That's just a silly stretch and logical, mathematical forumula is how we objectively describe the world and prove it exists at all.