As the title suggests, can anyone make a custom board that connects via a pcie connector? Do you need to purchase the rights/license to use it or is it all open to the public? For example my use cases would be communicating with an fpga that's on a custom board as well as communication between two of said boards.
You only absolutely need to pay money to PCI-SIG if you need your own vendor ID. If you’re using an FPGA, you can use the FPGA company’s vendor ID (for Xilinx, it’s 0x10EE).
Otherwise there’s no IP licensing to speak of. The specs are free download for PCI-SIG members, non-members pay a fee for them.