So no matter if the VA closes it on their end, the Veteran still has that year to file the appeal. They just have to file.
As for the foot question, it all depends on the service connected disability. If one is conneceted and the other is not, then the veteran needs to work to get them connected. As far as surgery is concerned, there are times it can make it worse. Thus resulting in a higher raiting if the veteran claims it. It would be based on how the VA rates said disability and if they are service connected or not (Secondary count also).
For the last question, you would not get rated for something without a diagnosis. You must see a doctor and you would need to have a diagnosis. Now you can claim said condition and they will send you to a doctor to see if you have said condtion. Then you have to hit the clausal elements to make sure they service connect it.
If you do not have medical evidence from when you were in, you can use Lay statements and buddy statements to show you had them in service. Or if you have a service connected condition that aggrivates your feet.