HTML5 semantic search results

1) I think you should stick with the article element, as

[t]he article element represents a self-contained composition in a document, page, application, or site and that is intended to be independently distributable or reusable [source]

You merely have a list of separate documents, so I think this is fully appropriate. The same is true for the front page of a blog, containing several posts with titles and outlines, each in a separate article element. Besides, if you intend to quote a few sentences of the articles (instead of providing summaries), you could even use blockquote elements, like in the example of a forum post showing the original posts a user is replying to.

2) If you're wondering if it's allowed to include article elements inside a li element, just feed it to the validator. As you can see, it is permitted to do so. Moreover, as the Working Draft says:

Contexts in which this element may be used:

3) I wouldn't use nav elements for those categories, as those links are not part of the main navigation of the page:

only sections that consist of major navigation blocks are appropriate for the nav element. In particular, it is common for footers to have a short list of links to various pages of a site, such as the terms of service, the home page, and a copyright page. The footer element alone is sufficient for such cases, without a nav element. [source]

4) Do not use the details and/or summary elements, as those are used as part of interactive elements and are not intended for plain documents.

UPDATE: Regarding if it's a good idea to use an (un)ordered list to present search results:

The ul element represents a list of items, where the order of the items is not important — that is, where changing the order would not materially change the meaning of the document. [source]

As a list of search results actually is a list, I think this is the appropriate element to use; however, as it seems to me that the order is important (I expect the best matching result to be on top of the list), I think that you should use an ordered list (ol) instead:

The ol element represents a list of items, where the items have been intentionally ordered, such that changing the order would change the meaning of the document. [source]

Using CSS you can simply hide the numbers.

EDIT: Whoops, I just realized you already use an ol (due to my fatique, I thought you used an ul). I'll leave my ‘update’ as is; after all, it might be useful to someone.