Can you use an X-ray to diagnose a PCL tear to see if you need reconstruction?

Maybe. The best diagnostic method is a good physical exam to determine how loose the knee is. Mri is the most detailed imaging that will tell you what ligaments are injured. An xray won't show you the PCL tear but it can show you how far back the tibia sits relative to the femur if you have a comparison view of the other knee and it is a dynamic view of someone pushing the leg back during xray.
Partially. While it may be possible to spot changes in the relationship between the femur and tibia on lateral xrays, usually an MRI is required to confirm the diagnosis of a PCL tear. Xray shows bones, MRI shows soft tissues such as ligaments, tendons, and menisci.
No. You can't see the PCL on an x-ray, but if the tibia (shin bone) is subluxed posteriorly on the lateral view, it suggests that the knee is unstable posteriorly and it might be because the PCL is torn. An MRI is a better than an x-ray to evaluate the pcl. Most PCL injuries can be managed nonoperatively with therapy. If you have done rehab and are still unstable, then consider surgery.