You can still get mainboards for modern CPUs (e.g. Intel Skylake) with PCI slots. Not sure how they work internally, e.g. if there is a PCIe bridge and if yes on what level PCI emulation happens.
PCI is a CPU-independent bus (unlike AT/ISA), it isn't really emulated, rather, there's a host bridge on these mainboards that connect it to PCIe from the CPU or southbridge.
No they don't make them any more. But my AMD64 machine from 2005 has AGP, IDE, and SATA. It's well supported by Fedora 25 which is a month old. Unless you're in new territory you have to decide what to support and will never gain traction due to the limited support.