I am no expert here as the large majority of my salted-paper prints are unsized. I have experimented with sizing using arrowroot starch or gelatin a bit, so take these comments with that caveat.
I have had better results using a smooth foam roller to apply sizing than I get with brushing it on.
When I coat, I don't worry too much if I miss a small spot on the edge of the paper, but I do try to coat the entire sheet. Remember that paper curls and buckles, etc. because the two faces of the paper react differently to moisture. Thus, I am hoping to avoid extra problems by having one side coated un-uniformly. Not sure that this is a real problem as I have not done a direct test.
As for using stainless steel, again no direct experiments. However, my chemist's intuition say it would be better to use glass than metal. With glass there is no possibility for the vessel to add redox active contaminants (i.e. metals) to you sizing. Again. I am not sure this is a real problem in practice, but it is one possible source of variation that is easy enough to avoid. My first rule of alt processes is "Avoid as many sources of variability as possible. There are plenty to go around as it is!".