When you quickly want to see a subset of a table, use a filter. You sometimes use the subset in another way (as input to a report, for example), so creating a query that you can name and execute makes more sense.
If I save a filter as a named query, what does the query's Query Design view look like?
Filters are less powerful than queries, but they are easier to designate . As you create more queries and get used to your data needs, you will find that many of your queries are little more than filters. Instead of messing with the Query Design view to design the query, generate a simpler Filter by Form filter and save it as a query. If you then want to modify the filter-based query or add more complex criteria, open the query's Query Design view and you can see that Access selected the proper source table and field names for you. You can then add to the criteria lines and request additional fields if you want.
Does the row on which I place criteria make a difference?
Yes, although you are getting into some confusing logic. The way you specify criteria between two fields often indicates how you want the combined criteria to work. If you place one field's criterion on the same row as another field's, an implied and relation takes place, and Access extracts only those records that contain a match for both criteria values. If you place one field's criterion on a different row from another field's, an implied or relation takes place between them.
How can I see my data in two ways, say, with the field names arranged alphabetically and with the fields arranged in the order of my table's design?
Create a query that extracts all the fields from your table. The query's output, or data subset, will contain all data that the original table contains. (The subset will be the same size as the table.) Set up the query's output for ordering the fields alphabetically. Queries aren't just for creating smaller subsets of tables; you can create a query to report table data in an order that differs from a table's original design order.