WordPress.org

Are favicons cached locally?

Yes. The actual images are cached in /blogroll-links-favicons/cache/. This is new in v2.0.

Some bookmarks aren't showing any icon at all, why?

Try refreshing the favicons. Go to Links > Link Favicons and choose the refresh cache option. This refreshes all favicons. To refresh a single favicon, open the edit page for that link and click "Update Link." Be careful, as page loads may slow to a crawl during this process which could last up to a minute or more if you've got a large number of links.

How often is the cache refreshed?

At this point, refreshes must be done manually.