For more on Google operators, visit http://support.google.com/websearch/bin/answer.py?hl=en&answer=136861.
You can do most of the functions above, without knowing the "operators," by using the Advanced Search screen. To access the Advanced Search, click the gear icon in the top right corner of the search results page then click Advanced search.
For more informaiton about how google works, visit http://www.google.com/competition/howgooglesearchworks.html.
You can also use Google to see what pages link to a specific address. To do this, simply type link: followed by the website address (with no spaces after the colon).
What's in a name? For help understanding what the different domain extensions tell about a website, visit the ISO's decoding table.