DomBuddy.com is a free domain name search suite, available as an online domain search tool and a desktop application for Microsoft Windows and MacOS X.

The domain name generator on DomBuddy.com provides a range of search tools developed to find available domain names. You may use the Random Syllables (“Random”) domain name generator to generate totally random domain names that don't make sense, but sound English and may be brandable. The premium search tool helps you to find domain names that contain actual search phrases, and using that tool you might actually discover some niches. The Keywords Tool and the Idea Finder module (called “Combine” in the deskop application”) combine keywords, keyword lists as well as prefixes and suffixes – those are most useful if you already have an idea of what your domain name should look like.

Sure. You may either use the single domain name search/quick check function or the Bulk Check (“Bulk” in the desktop application) to enter some domain names to check whether those are available for registration.