I think this is one scenario where we wouldn't guarantee the same order, except in certain cases. You have the same number of features going in and coming out, so you could set Group By Mode to "Process When Group Changes" and that would give you the same input and output.

But that would not usually be the case. Most people are aggregating multiple features and not in a specific order. So that's why the default is to not worry about the order.

So, as long as you are aggregating data that's already in group order, you can change that parameter and get what you need.

Is it possible to number based on the y-coordinates value (descending) such that the highest y-coordinate takes number 1 and so forth?

Yes, you can use a Sorter to sort on that attribute and then a Counter.

Thank you for the help