I believe your question is about 2 way searching of SharePoint applications.
Search other applications or sites from SharePoint
Federated search can be used to search external sites for SharePoint. You can point any external site or web application for SharePoint to crawl. SharePoint crawler will crawl the website whatever it has access to, probably as an anonymous user. The crawled results would be displayed in subsequent search results.
Searching into SharePoint applications
Other search bots like google and yahoo can also crawl SharePoint site contents by default for any anonymous site. In this case, crawling in the SharePoint sites by these bots can be managed by using a Robots.txt file.
If you need to search from your custom .Net web application, you can utilize the search functionality of SharePoint inside your application. There is an excellent post from Andrew Connell to help you with that.