Yes, you can easily change those functions to point at other columns.
1) For the Sort. If you look at the items property of the Gallery you will see something that looks like the following:
SortByColumns(Filter([@Dogs], StartsWith(Title, TextSearchBox1.Text)), "Title", If(SortDescending1, SortOrder.Descending, SortOrder.Ascending))
where [@Dogs] is my list. Simple change the "Title" entry to the name of a different sortable column, like another single line of text.
2) for Search. In the same property you see the function StartsWith(). The first entry is Title. Change that to a different single line of text column and you will be able to search on it.