If you do not do a proper redirection, your sites may get penalized by the search engines. A 301 permanent redirect is required. Most redirections generate a 302 temporary redirect code, which can result in sites being duplicated under multiple domains. You never want to do this because mirror sites get penalized.

Search engine submissions are no longer necessary. Just build a few links to the sites and the search engines will find it. If you do decide to submit, http://subdomain.blogspot.com is considered to be a different site than http://www.blogspot.com because subdomains can exist on different servers. The search engine won't necessarily find the subdomain unless you provide links to it or submit it separately.