I'm opening this with APG because most of the question pertains to the use of landmarks. If there is a more appropriate place for this discussion, please let me know.

I'm doing some work on a search component inside the top navigation on a site.
Currently it is implemented as a search input inside a search region. To meet the requirements for labelling, the input and region are both called "search". It results in a bit of verbosity for a screen reader.
It's easy enough for me to get them to either remove the label for the search region, which is obviously fully redundant, or make it more specific, like "site". However, I'm wondering if it is necessary or even advisable to use the search region in a banner situation. Some conversations with others suggests that the use of the search region is a little over-prescribed. Search is conventionally located in the banner, and the banner does not tend to have enough in it such that a user cannot just navigate to the banner to get to the search. Is the use of a search input without a nesting banner considered a problem in this context?

The second part of this question involves scenarios where there is a second search area in the page, in addition to the banner search. In such a situation, each should arguably be uniquely named to help users differentiate. Because search fields on the whole do not have visible labels but do have placeholder text, I'm wondering if there are any concerns with using the placeholder value as the default label for the inputs themselves? It is rare, in my experience that the same placeholder would be used in both search inputs.

In regard to the search region, if the banner search is not put inside a search region but the one in the main content space is, this reduces the need to uniquely name each, and also addresses what is arguably the more important affordance (getting to the page search, since the search in the banner is already easy to locate and navigate to). Optionally, the same name can be used for both the input and the region in each case, but that just creates more repetition.

Any comments on this approach in regard to best practices?