The reason or grounds for the appeal in the foreclosure case do not matter because this question assumes that 1. A stay awaiting an appeal is not granted and 2. The appeals court rules in my favor that I was correct that the Court was in error in setting the foreclosure sale in the manner it did.
The reason for the question is that I am trying to determine other than the satisfaction of knowing I was right, what do I have to gain because if there is no stay awaiting appeal, I am put out of the house. Will this ruling in my favor essentially invalidate the sale? This will aid me little because the sale could just be rescheduled but can it effect the buyer of the property at the foreclosure sale? Also, would the fact that the property is already sold make my appeal moot?
Stays are not routinely granted to stop the underlying case. Sometimes the appellate court will require a supersedeas bond to get a stay in foreclosure cases; if you are prepared to part with thousands or tens of thousand temporarily to get a stay it could be an option.
Without a stay, and if the appellate court reverses, the new purchaser will be forced to turn back over possession if the sale is invalidated. You don't have a lot to gain other than more costs and fees; because even if you are "right" the judgment is in place and a new sale date will just be rescheduled upon remand.
The only way the appeal is moot is if the order you are challenging, which sounds like the order rescheduling the sale, is more than 30 days ago. If so, you may have lost your right to appeal.
You need to see a lawyer who does appeals ASAP.
I don't think an order to schedule the foreclosure sale can be appealed. Perhaps it can under a writ of certiorari. It sounds like you don't know what you are doing in the appeal. Get some legal advice before wasting more time and effort on this appeal. The orders underlying most pro se appeals are affirmed because... well the reasons go on and on. Pro se appellants usually don't know what is appealable. They don't know what the standard of review is. They don't know how to frame the issues. They don't know how to research the law. Here, you probably filed the wrong type of appeal. You should have filed a petition fore certiorari, and I am guessing you filed a "Notice of Appeal."
But to answer your question, your appeal would not be "mooted" by an incorrect sale. The sale could just be reversed with and the trial court would probably have to resell the property in the unlikely event that you prevail upon appeal. I don't say this to be mean. I say this because I see so many pro se appellate briefs in foreclosure that had a good chance of success if the homeowner knew how to preserve, frame, support and write about the issues that matter. It is truly frustrating to see a good case go bad simply because it is in the (usually incompetent) hands of a pro se party.