What are the benefits of inserting the date and a page number as opposed to typing the date?

If you put it in in the automated fashion, it will keep updating the date, so that every time you print it, it will have the date of that day. Sometimes you want to do that, whereas other times you want to always have the original date. That is when you would type it in.

With page numbers, they will automatically update as a document changes and put new page numbers in automatically as it gets bigger, saving you the need to do it.