I am trying to understand how PCI Express works so i can write a windows driver that can read and write to a custom PCI Express device with no on-board memory.
I underst
From your query its clear that you want to write a driver for a PCIe slave device. To understand the scheme of things happening behind PCIe transfer, a lot of stuff is available on internet (Like PCIe Bus Enumeration, Peripheral Address Mapping to the memory etc).
Yes your understanding is correct regarding the mapping of PCIe registers to the memory and you can read/write them.( For e.g in case of linux PCIe device driver you can do this using "ioremap" ).
An address bus is used to specify a physical address. When a processor or DMA-enabled device needs to read or write to a memory location, it specifies that memory location on the address bus. Nothing more to add to that. "PCIe bus enumeration" topic will answer your 2nd question.
Your third question is vague. You mean slave PCIe device. Assuming it is, yes you can transfer data between a slave PCIe device and host using a DMA controller. I am working on a project which involves "PCIe-DMA" connected with the host over the PCIe bus. Really depends on your design and implementation. So in my case PCIe-DMA is itself a slave PCIe device on the target board connected to the host over PCIe.