These are interesting questions, but not being a scientist I'm not going to try to address such fine lines of distinction. I'm surprised to see you allude to ghosts, and I suspect you don't really think it's a "ghost," any more than I do.
Indeed, I don't believe they exist at all; it was a hypothetical. Regardless of whether or not ghosts exist, they are traditionally deemed spiritual, supernatural, paranormal, etc. This suggests that the different between 'physical' and 'spiritual' is a traditional one, not one that has any actual meaning. Why are ghosts spiritual and neutrinos physical? What is it about them that separates them so?
If you think it's difficult trying to create a line of demarcation between physical and Spiritual, you should try doing it between Spirit and soul!
Spiritual Truth does not try to address scientific pursuit. Your questions here are clearly not of the Spiritual realm.
On the contrary, you were the one how asserted a demarcation between the physical and spiritual. If you don't know what the difference is, how do you know there's a difference at all?
Let's look at it another way. Science is the pursuit of knowledge, a way of accruing facts and using them to support or disprove explanations or claims about the universe ("Pluto exists, and here are the facts", "
Tiktaalik exists, and here are the facts"). You say that science can't go beyond the physical, the natural, etc. Thus, we can deduce what the 'physical' is. As the physical is anything and everything that's within the bounds of science, and since science is the pursuit of verifiable knowledge, we can therefore say that something is 'physical' if it can be scientifically studied, if its existence can be supported with data.
Ghosts, for instance, therefore become 'physical'. If they exist as traditionally understood, their existence can be proven and they can be scientifically studied - by your own definition, this places them squarely in the realm of the physical, natural world.
Since you define science as being restricted to the physical world, would you say the above is a reasonable definition of 'physical'?