Because many pages on your site probably contain links to other pages on your site, it's best to exclude those if possible. The search will work even if you don't have your own domain name. Unfortunately, the HotBot search will work only if you have your own domain name. It's a good idea to try all three search engines, because each will list pages that the others missed. The idea is that some visitors to site A will find site B, and vice versa.
Reciprocal links are desirable only if the two parties benefit equally.
If you make a link to the White House, you shouldn't expect the White House to reciprocate. If you do have external links on your site, check them regularly to see that they still work. Because the Web is in constant flux, old links are often broken links. The URL for the home page of a large organization is likely to be usable indefinitely, but URLs for other pages can stop working if the page is moved or deleted when the site is reorganized. It's not necessary to ask permission to make a link, any more than it's necessary to get permission from a publisher to cite a reference.