Window fallen out
Thanks for posting. I don't think we have this exact hinge set, but look at our 36-048. I think this will work just as well.
I'm not sure about the operator. Could I see a photo of it out of the window? Can you also tell me the length of that link arm?
Ah, I see. There may be something else holding the operator in, but I'm not sure what. It's a bit of an odd design. We did find a pair that are similar that I think can work: our 39-315 and 39-316. The only catch is that the link arm is 1" shorter.
That might not be the end of the world, though. Your window won't open quite as much, and in a worst case scenario you may need to remount the bracket to which the arm attaches (you can see it in your second photo in your first post).
Another detail to consider is that it won't have the same nesting cover/handle combo as your operator now. The covers for the 39-315 and 39-316 are built into the operator and cannot be removed at all. With this in mind, you'll want a new handle, since your old one will look awkward on this style; I recommend our 39-205.
I'm not sure you'll have to replace the whole window. That seems like overkill. If the hinges and operators are the only problem then I think you can get away just replacing those parts.