i dont think there is any need to add to google because they would themselves crawl and get your site thmselves thanks, ankur
You must submit it to Google to get indexed faster. Your site could be found from backlinks on other sites but it would take forever. Submit a XML sitemap at google webmaster tools. Also make sure to verify your site there too. If you need to have a sitemap made for you for free do a search for "XML sitemaps"
It depends, According to my experience if your site is not indexed within a week than u will have to submit it to google. If u want ur site to be indexed quickly than submit your site to google as well as other search engines such as yahoo, msn, alexa, etc and also do some directory submission and surely your site will be indexed with in 2-3 days. hopes this information will help u...