Hello,
Since we have different part numbers than the manufacturers of your hardware, we'll need to see a picture of the part you're trying to replace, as well as dimensions. I've associated one of our common 10" hinge sets to get you started. Thank you!
I do believe you can use the 36-048 hinge set as a replacement for the one you show in your photos. As for the operator, we carry the newer type with the rounded type body. You have the older rectangular type. Take a look at the 39-315 and the 39-316. They have a "link" arm that looks like the same length as yours. However the arm is riveted to the top of the gear arm where your link arm is attached at the bottom. Not sure if this arm being at the top will hit something in the window when you go to close the window. We also carry the 39-171 and 39-172 operator with the off set link arm. Either one of these type operators should fit your window, but you might have to adapt them a little to operator your window. Take a look at the suggested operators along with the related hardware and videos.