USB C is a connector and cable. You can use it with USB 1.1 FS is you're so inclined; it'll work just fine. (In fact, I'd recommend sticking to C connectors when possible.)
USB 3 is a standard that includes USB A, B, and C connectors, their interoperability and backwards compatibility with equipment that implements previous versions of USB.
USB PD relies entirely on the USB CC pins for negotiation and doesn't use the D pairs. It requires USB 3 on both ends, relying solely on the USB C CC pins either using protocol based negotiation or resistors, or both.
USB A and B can't support USB PD, but cables and your little adapter can internally terminate the CC pins in resistors, or implement USB PD on behalf of a device. Possibly on behalf of a host (with a suitable power supply, though this might be sketchy). This is easy since only the CC pins are used.
If you have a USB C connector you SHOULD terminate the CC pins properly so the other end can sense orientation. This means on the upstream (host facing) port the CC pins should be pulled down (device impersonation), on the downstream (device facing) port pulled up (host impersonation). This in turn means your adapter is going to be directional, with a host-facing side and a device-facing side. Since USB A port/cable connectors are different this is probably already the case.